|
(inexact_reduce
(lower_validity_TCC1 0
(lower_validity_TCC1-1 nil 3397984485 ("" (subtype-tcc) nil nil)
((enabled const-decl "finite_set[below(S)]" fault_assumptions_stage
nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil)
(enabled_within? const-decl "bool" fault_assumptions_stage nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(correct_lower_inaccuracy? const-decl "bool" inexact_comm_stage
nil)
(empty? const-decl "bool" sets nil)
(quorum? const-decl "bool" pigeonhole nil)
(quorum? const-decl "bool" fault_assumptions_stage nil)
(quorum_lower? const-decl "bool" inexact_comm_stage nil)
(quorum_lower? const-decl "bool" inexact_comm nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(<= const-decl "bool" reals nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(protocol const-decl "bool" protocol nil))
nil))
(lower_validity_TCC2 0
(lower_validity_TCC2-1 nil 3397984485 ("" (subtype-tcc) nil nil)
((NOT const-decl "[bool -> bool]" booleans nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(enabled const-decl "finite_set[below(S)]" fault_assumptions_stage
nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil)
(enabled_within? const-decl "bool" fault_assumptions_stage nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(correct_lower_inaccuracy? const-decl "bool" inexact_comm_stage
nil)
(empty? const-decl "bool" sets nil)
(quorum? const-decl "bool" pigeonhole nil)
(quorum? const-decl "bool" fault_assumptions_stage nil)
(quorum_lower? const-decl "bool" inexact_comm_stage nil)
(quorum_lower? const-decl "bool" inexact_comm nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(<= const-decl "bool" reals nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(protocol const-decl "bool" protocol nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(lower_validity 0
(lower_validity-2 nil 3398099576
("" (induct "k")
(("1" (skosimp*)
(("1" (expand "sigma") (("1" (assert) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (inst?)
(("2" (inst?)
(("2" (inst?)
(("2" (inst - "eps_l!1" _)
(("2" (inst?)
(("2" (assert)
(("2" (prop)
(("1" (rewrite "sigma_last" +)
(("1"
(invoke
(then (case "%1 - eps_l!1(j!1+j!2) <= %2")
(assert))
(! -1 r) (! 1 r))
(("1" (hide 2 -1)
(("1" (expand "enabled_within?")
(("1" (expand "protocol")
(("1"
(expand "quorum_lower?")
(("1"
(inst - "j!1 + j!2")
(("1"
(inst - "j!1 + j!2")
(("1"
(inst - "j!1 + j!2")
(("1"
(assert)
(("1"
(expand "v_min")
(("1"
(expand "reduce_choice")
(("1"
(replace -1 :hide? t)
(("1"
(lemma
"reduce_min_validity[N(j!2 + j!1), N(1 + j!1 + j!2), error(j!1 + j!2)]")
(("1"
(inst?)
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide-all-but (1 -1))
(("2" (expand "protocol")
(("2" (skosimp*)
(("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil)
("3" (hide-all-but (1 -2))
(("3" (expand "quorum_lower?")
(("3" (skosimp*)
(("3" (inst?) (("3" (assert) nil nil)) nil))
nil))
nil))
nil)
("4" (hide-all-but (1 -3))
(("4" (expand "enabled_within?")
(("4" (skosimp*)
(("4" (inst?) (("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil))
nil))
nil)
((sigma_last formula-decl nil sigma "reals/")
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(reduce_min_validity formula-decl nil inexact_reduce_stage nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(odd_plus_odd_is_even application-judgement "even_int" integers
nil)
(sigma_nnreal application-judgement "nnreal" sigma_nat "reals/")
(nat_induction formula-decl nil naturalnumbers nil)
(sigma def-decl "real" sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(T_low type-eq-decl nil sigma "reals/")
(v_min const-decl "T" k_ordered nil)
(pred type-eq-decl nil defined_types nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(ne_seqs type-eq-decl nil seqs "structures/")
(AND const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil)
(below type-eq-decl nil nat_types nil)
(finite_sequence type-eq-decl nil finite_sequences nil)
(> const-decl "bool" reals nil) (< const-decl "bool" reals nil)
(dom type-eq-decl nil min_seq "structures/")
(= const-decl "[T, T -> boolean]" equalities nil)
(min const-decl "{t: T |
(FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_seq
"structures/")
(dom type-eq-decl nil max_seq "structures/")
(max const-decl "{t: T |
(FORALL (ii: dom(s)): seq(s)(ii) <= t) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" max_seq
"structures/")
(consensus_function type-eq-decl nil ordered_finite_sequences nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(k_consensus_function type-eq-decl nil k_ordered nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(below type-eq-decl nil naturalnumbers nil)
(check_stage type-eq-decl nil node_functions_stage nil)
(check_function type-eq-decl nil node_functions nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(set type-eq-decl nil sets nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(empty? const-decl "bool" sets nil)
(non_empty_finite_set type-eq-decl nil finite_sets nil)
(rcvd_matrix_stage type-eq-decl nil node_functions_stage nil)
(rcvd_matrix type-eq-decl nil node_functions nil)
(sent_vec_stage type-eq-decl nil node_functions_stage nil)
(sent_vec type-eq-decl nil node_functions nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(tau_type type-eq-decl nil tau_declaration nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(result_vec_stage type-eq-decl nil node_functions_stage nil)
(choice_stage type-eq-decl nil node_functions_stage nil)
(choice_function type-eq-decl nil node_functions nil)
(protocol const-decl "bool" protocol nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(quorum_lower? const-decl "bool" inexact_comm nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil)
(lower_validity-1 nil 3397985916
("" (induct "k")
(("1" (skosimp*)
(("1" (expand "sigma") (("1" (assert) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (inst?)
(("2" (inst?)
(("2" (inst?)
(("2" (inst - "eps_l!1" _)
(("2" (inst?)
(("2" (assert)
(("2" (prop)
(("1" (rewrite "sigma_last" +)
(("1"
(invoke
(then (case "%1 - eps_l!1(j!1+j!2) <= %2")
(assert))
(! -1 r) (! 1 r))
(("1" (hide 2 -1)
(("1" (expand "enabled_within?")
(("1" (expand "protocol")
(("1"
(expand "generalized_majority_lower?")
(("1"
(inst - "j!1 + j!2")
(("1"
(inst - "j!1 + j!2")
(("1"
(inst - "j!1 + j!2")
(("1"
(assert)
(("1"
(expand "v_min")
(("1"
(expand "reduce_select")
(("1"
(replace -1 :hide? t)
(("1"
(lemma
"reduce_min_validity[N(j!2 + j!1), N(1 + j!1 + j!2), error(j!1 + j!2)]")
(("1"
(inst?)
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide-all-but (1 -1))
(("2" (expand "protocol")
(("2" (skosimp*)
(("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil)
("3" (hide-all-but (1 -2))
(("3" (expand "generalized_majority_lower?")
(("3" (skosimp*)
(("3" (inst?) (("3" (assert) nil nil)) nil))
nil))
nil))
nil)
("4" (hide-all-but (1 -3))
(("4" (expand "enabled_within?")
(("4" (skosimp*)
(("4" (inst?) (("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil))
nil))
nil)
((sigma_last formula-decl nil sigma "reals/")
(reduce_min_validity formula-decl nil inexact_reduce_stage nil)
(sigma def-decl "real" sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(T_low type-eq-decl nil sigma "reals/")
(v_min const-decl "T" k_ordered nil)
(check_stage type-eq-decl nil node_functions_stage nil)
(check_function type-eq-decl nil node_functions nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(non_empty_finite_set type-eq-decl nil finite_sets nil)
(rcvd_matrix_stage type-eq-decl nil node_functions_stage nil)
(rcvd_matrix type-eq-decl nil node_functions nil)
(sent_vec_stage type-eq-decl nil node_functions_stage nil)
(sent_vec type-eq-decl nil node_functions nil)
(Card const-decl "nat" finite_sets nil)
(card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
(result_vec_stage type-eq-decl nil node_functions_stage nil)
(choice_stage type-eq-decl nil node_functions_stage nil)
(choice_function type-eq-decl nil node_functions nil))
nil))
(upper_validity_TCC1 0
(upper_validity_TCC1-1 nil 3397984485 ("" (subtype-tcc) nil nil)
((enabled const-decl "finite_set[below(S)]" fault_assumptions_stage
nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil)
(enabled_within? const-decl "bool" fault_assumptions_stage nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(correct_upper_inaccuracy? const-decl "bool" inexact_comm_stage
nil)
(empty? const-decl "bool" sets nil)
(quorum? const-decl "bool" pigeonhole nil)
(quorum? const-decl "bool" fault_assumptions_stage nil)
(quorum_upper? const-decl "bool" inexact_comm_stage nil)
(quorum_upper? const-decl "bool" inexact_comm nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(<= const-decl "bool" reals nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(protocol const-decl "bool" protocol nil))
nil))
(upper_validity_TCC2 0
(upper_validity_TCC2-1 nil 3397984485 ("" (subtype-tcc) nil nil)
((NOT const-decl "[bool -> bool]" booleans nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(enabled const-decl "finite_set[below(S)]" fault_assumptions_stage
nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil)
(enabled_within? const-decl "bool" fault_assumptions_stage nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(correct_upper_inaccuracy? const-decl "bool" inexact_comm_stage
nil)
(empty? const-decl "bool" sets nil)
(quorum? const-decl "bool" pigeonhole nil)
(quorum? const-decl "bool" fault_assumptions_stage nil)
(quorum_upper? const-decl "bool" inexact_comm_stage nil)
(quorum_upper? const-decl "bool" inexact_comm nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(<= const-decl "bool" reals nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(protocol const-decl "bool" protocol nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(upper_validity 0
(upper_validity-3 nil 3403269169
("" (induct "k")
(("1" (skosimp*)
(("1" (expand "sigma") (("1" (assert) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (inst?)
(("2" (inst?)
(("2" (inst?)
(("2" (inst - "eps_u!1" "rcvd!1")
(("2" (assert)
(("2" (prop)
(("1" (rewrite "sigma_first" 1)
(("1"
(invoke
(then (case "%1 <= %2 + eps_u!1(j!2)") (assert))
(! -1 r 1) (! 1 r 1))
(("1" (hide 2 -1)
(("1" (expand "enabled_within?")
(("1" (expand "quorum_upper?")
(("1" (expand "protocol")
(("1"
(inst - "j!2")
(("1"
(inst - "j!2")
(("1"
(inst - "j!2")
(("1"
(assert)
(("1"
(expand "v_max")
(("1"
(expand "reduce_choice")
(("1"
(replace -1 :hide? t)
(("1"
(lemma
"reduce_max_validity[N(j!2), N(1 + j!2), error(j!2)]")
(("1"
(inst?)
(("1"
(inst?)
(("1"
(inst?)
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide-all-but (1 -1))
(("2" (expand "protocol")
(("2" (skosimp*)
(("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil)
("3" (hide-all-but (1 -2))
(("3" (expand "quorum_upper?")
(("3" (skosimp*)
(("3" (inst?) (("3" (assert) nil nil)) nil))
nil))
nil))
nil)
("4" (hide-all-but (1 -3))
(("4" (expand "enabled_within?")
(("4" (skosimp*)
(("4" (inst?) (("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil))
nil))
nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(reduce_max_validity formula-decl nil inexact_reduce_stage nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(sigma_first formula-decl nil sigma "reals/")
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(odd_plus_odd_is_even application-judgement "even_int" integers
nil)
(sigma_nnreal application-judgement "nnreal" sigma_nat "reals/")
(nat_induction formula-decl nil naturalnumbers nil)
(sigma def-decl "real" sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(T_low type-eq-decl nil sigma "reals/")
(v_max const-decl "T" k_ordered nil)
(pred type-eq-decl nil defined_types nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(ne_seqs type-eq-decl nil seqs "structures/")
(AND const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil)
(below type-eq-decl nil nat_types nil)
(finite_sequence type-eq-decl nil finite_sequences nil)
(> const-decl "bool" reals nil) (< const-decl "bool" reals nil)
(dom type-eq-decl nil min_seq "structures/")
(= const-decl "[T, T -> boolean]" equalities nil)
(min const-decl "{t: T |
(FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_seq
"structures/")
(dom type-eq-decl nil max_seq "structures/")
(max const-decl "{t: T |
(FORALL (ii: dom(s)): seq(s)(ii) <= t) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" max_seq
"structures/")
(consensus_function type-eq-decl nil ordered_finite_sequences nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(k_consensus_function type-eq-decl nil k_ordered nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
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(below type-eq-decl nil naturalnumbers nil)
(check_stage type-eq-decl nil node_functions_stage nil)
(check_function type-eq-decl nil node_functions nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(set type-eq-decl nil sets nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(empty? const-decl "bool" sets nil)
(non_empty_finite_set type-eq-decl nil finite_sets nil)
(rcvd_matrix_stage type-eq-decl nil node_functions_stage nil)
(rcvd_matrix type-eq-decl nil node_functions nil)
(sent_vec_stage type-eq-decl nil node_functions_stage nil)
(sent_vec type-eq-decl nil node_functions nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(tau_type type-eq-decl nil tau_declaration nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(result_vec_stage type-eq-decl nil node_functions_stage nil)
(choice_stage type-eq-decl nil node_functions_stage nil)
(choice_function type-eq-decl nil node_functions nil)
(protocol const-decl "bool" protocol nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(quorum_upper? const-decl "bool" inexact_comm nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_plus_real_is_real application-judgement "real" reals nil))
nil)
(upper_validity-2 nil 3398099607
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("2" (skosimp*)
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(("1" (rewrite "sigma_first" 1)
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(("1" (hide 2 -1)
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(("1" (expand "quorum_upper?")
(("1" (expand "protocol")
(("1"
(inst - "j!2")
(("1"
(inst - "j!2")
(("1"
(inst - "j!2")
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(("1"
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(("1"
(inst?)
(("1"
(inst?)
(("1"
(inst?)
(("1"
(assert)
nil
nil))
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nil))
nil))
nil))
nil))
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nil)
("2" (hide-all-but (1 -1))
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(("2" (skosimp*)
(("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil)
("3" (hide-all-but (1 -2))
(("3" (expand "quorum_upper?")
(("3" (skosimp*)
(("3" (inst?) (("3" (assert) nil nil)) nil))
nil))
nil))
nil)
("4" (hide-all-but (1 -3))
(("4" (expand "enabled_within?")
(("4" (skosimp*)
(("4" (inst?) (("4" (assert) nil nil)) nil))
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nil))
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nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil))
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nil)
((enabled_within? const-decl "bool" inexact_comm nil)
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(choice_stage type-eq-decl nil node_functions_stage nil)
(result_vec_stage type-eq-decl nil node_functions_stage nil)
(card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
(Card const-decl "nat" finite_sets nil)
(sent_vec type-eq-decl nil node_functions nil)
(sent_vec_stage type-eq-decl nil node_functions_stage nil)
(rcvd_matrix type-eq-decl nil node_functions nil)
(rcvd_matrix_stage type-eq-decl nil node_functions_stage nil)
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(finite_set type-eq-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(check_function type-eq-decl nil node_functions nil)
(check_stage type-eq-decl nil node_functions_stage nil)
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(T_low type-eq-decl nil sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(sigma def-decl "real" sigma "reals/")
(sigma_first formula-decl nil sigma "reals/")
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nil)
(upper_validity-1 nil 3397985929
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(("1" (expand "sigma") (("1" (assert) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (inst?)
(("2" (inst?)
(("2" (inst?)
(("2" (inst - "eps_u!1" "rcvd!1")
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(("1" (rewrite "sigma_first" 1)
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(invoke
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(("1" (hide 2 -1)
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(("1"
(inst - "j!2")
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(("1"
(inst?)
(("1"
(inst?)
(("1"
(inst?)
(("1"
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nil
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nil))
nil))
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("2" (hide-all-but (1 -1))
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("3" (hide-all-but (1 -2))
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(("3" (skosimp*)
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nil))
nil)
("4" (hide-all-but (1 -3))
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(("4" (skosimp*)
(("4" (inst?) (("4" (assert) nil nil)) nil))
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nil))
nil))
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nil))
nil))
nil)
("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil))
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((reduce_max_validity formula-decl nil inexact_reduce_stage nil)
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(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
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(rcvd_matrix type-eq-decl nil node_functions nil)
(sent_vec_stage type-eq-decl nil node_functions_stage nil)
(sent_vec type-eq-decl nil node_functions nil)
(Card const-decl "nat" finite_sets nil)
(card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
(result_vec_stage type-eq-decl nil node_functions_stage nil)
(choice_stage type-eq-decl nil node_functions_stage nil)
(choice_function type-eq-decl nil node_functions nil))
nil))
(agreement_propagation_TCC1 0
(agreement_propagation_TCC1-1 nil 3397984485
("" (subtype-tcc) nil nil)
((v_max const-decl "T" select_minmax nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
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(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
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(boolean nonempty-type-decl nil booleans nil)
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(v_max const-decl "T" k_ordered nil)
(v_min const-decl "T" select_minmax nil)
(v_min const-decl "T" k_ordered nil)
(enabled const-decl "finite_set[below(S)]" fault_assumptions_stage
nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil)
(enabled_within? const-decl "bool" fault_assumptions_stage nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(correct_imprecision? const-decl "bool" inexact_comm_stage nil)
(empty? const-decl "bool" sets nil)
(quorum? const-decl "bool" pigeonhole nil)
(quorum? const-decl "bool" fault_assumptions_stage nil)
(quorum_imprecision? const-decl "bool" inexact_comm_stage nil)
(quorum_imprecision? const-decl "bool" inexact_comm nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(protocol const-decl "bool" protocol nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil))
nil))
(agreement_propagation_TCC2 0
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("" (subtype-tcc) nil nil)
((nonneg_real nonempty-type-eq-decl nil real_types nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(finite_image application-judgement "finite_set[R]"
function_image_aux nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(v_max const-decl "T" select_minmax nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(<= const-decl "bool" reals nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(v_max const-decl "T" k_ordered nil)
(v_min const-decl "T" select_minmax nil)
(v_min const-decl "T" k_ordered nil)
(enabled const-decl "finite_set[below(S)]" fault_assumptions_stage
nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil)
(enabled_within? const-decl "bool" fault_assumptions_stage nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(correct_imprecision? const-decl "bool" inexact_comm_stage nil)
(empty? const-decl "bool" sets nil)
(quorum? const-decl "bool" pigeonhole nil)
(quorum? const-decl "bool" fault_assumptions_stage nil)
(quorum_imprecision? const-decl "bool" inexact_comm_stage nil)
(quorum_imprecision? const-decl "bool" inexact_comm nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(protocol const-decl "bool" protocol nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(agreement_propagation 0
(agreement_propagation-4 nil 3403269194
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(("1" (skosimp*)
(("1" (expand "sigma") (("1" (propax) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (inst?)
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(("2" (inst?)
(("2" (inst - "epsilon!1" "rcvd!1")
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(lemma
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(inst
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_
_
"delta!1+sigma(j!2,j!1+j!2-1,epsilon!1)"
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"epsilon!1(j!1+j!2)"
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(("1"
(inst?)
(("1"
(assert)
(("1"
(inst?)
(("1"
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(("1"
(rewrite
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nil
nil))
nil))
nil))
nil))
nil)
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(hide-all-but 1)
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(assert)
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(use
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(("1"
(skosimp*)
(("1"
(assert)
nil
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("2"
(ground)
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(ground)
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nil)
("2" (hide-all-but (1 -1))
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(("2" (skosimp*)
(("2" (inst?) (("2" (assert) nil nil)) nil))
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("3" (hide-all-but (1 -2))
(("3" (expand "quorum_imprecision?")
(("3" (skosimp*)
(("3" (inst?) (("3" (assert) nil nil)) nil))
nil))
nil))
nil)
("4" (hide-all-but (1 -3))
(("4" (expand "enabled_within?")
(("4" (skosimp*)
(("4" (inst?) (("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide-all-but 1)
(("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil))
nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(j!1 skolem-const-decl "nat" inexact_reduce nil)
(j!2 skolem-const-decl "nat" inexact_reduce nil)
(sigma_last formula-decl nil sigma "reals/")
(sigma_nonneg formula-decl nil sigma "reals/")
(agreement_propagation formula-decl nil inexact_reduce_stage nil)
(odd_plus_odd_is_even application-judgement "even_int" integers
nil)
(sigma_nnreal application-judgement "nnreal" sigma_nat "reals/")
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(sigma def-decl "real" sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(T_low type-eq-decl nil sigma "reals/")
(pred type-eq-decl nil defined_types nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(ne_seqs type-eq-decl nil seqs "structures/")
(AND const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil)
(below type-eq-decl nil nat_types nil)
(finite_sequence type-eq-decl nil finite_sequences nil)
(> const-decl "bool" reals nil) (< const-decl "bool" reals nil)
(dom type-eq-decl nil min_seq "structures/")
(= const-decl "[T, T -> boolean]" equalities nil)
(min const-decl "{t: T |
(FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_seq
"structures/")
(dom type-eq-decl nil max_seq "structures/")
(max const-decl "{t: T |
(FORALL (ii: dom(s)): seq(s)(ii) <= t) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" max_seq
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(consensus_function type-eq-decl nil ordered_finite_sequences nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "[nat -> posnat]" inexact_reduce nil)
(error formal-const-decl "[nat -> real]" inexact_reduce nil)
(k_consensus_function type-eq-decl nil k_ordered nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(below type-eq-decl nil naturalnumbers nil)
(check_stage type-eq-decl nil node_functions_stage nil)
(check_function type-eq-decl nil node_functions nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(set type-eq-decl nil sets nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(empty? const-decl "bool" sets nil)
(non_empty_finite_set type-eq-decl nil finite_sets nil)
(rcvd_matrix_stage type-eq-decl nil node_functions_stage nil)
(rcvd_matrix type-eq-decl nil node_functions nil)
(sent_vec_stage type-eq-decl nil node_functions_stage nil)
(sent_vec type-eq-decl nil node_functions nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(tau_type type-eq-decl nil tau_declaration nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(result_vec_stage type-eq-decl nil node_functions_stage nil)
(choice_stage type-eq-decl nil node_functions_stage nil)
(choice_function type-eq-decl nil node_functions nil)
(protocol const-decl "bool" protocol nil)
(reduce_choice const-decl "choice_function" k_ordered nil)
(quorum_imprecision? const-decl "bool" inexact_comm nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(v_max const-decl "T" k_ordered nil)
(v_min const-decl "T" k_ordered nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil))
nil)
(agreement_propagation-3 nil 3398099716
("" (induct "k")
(("1" (skosimp*)
(("1" (expand "sigma") (("1" (propax) nil nil)) nil)) nil)
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"delta!1+sigma(j!2,j!1+j!2-1,epsilon!1)"
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"epsilon!1(j!1+j!2)"
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(("1"
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(("1"
(assert)
(("1"
(inst?)
(("1"
(assert)
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(rewrite
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nil))
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nil)
("2"
(hide-all-but 1)
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(flatten)
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nil)
("3" (hide-all-but (1 -2))
(("3" (expand "quorum_imprecision?")
(("3" (skosimp*)
(("3" (inst?) (("3" (assert) nil nil)) nil))
nil))
nil))
nil)
("4" (hide-all-but (1 -3))
(("4" (expand "enabled_within?")
(("4" (skosimp*)
(("4" (inst?) (("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide-all-but 1)
(("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil))
nil)
((v_min const-decl "T" k_ordered nil)
(v_max const-decl "T" k_ordered nil)
(enabled_within? const-decl "bool" inexact_comm nil)
(quorum_imprecision? const-decl "bool" inexact_comm nil)
(choice_function type-eq-decl nil node_functions nil)
(choice_stage type-eq-decl nil node_functions_stage nil)
(result_vec_stage type-eq-decl nil node_functions_stage nil)
(card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
(Card const-decl "nat" finite_sets nil)
(sent_vec type-eq-decl nil node_functions nil)
(sent_vec_stage type-eq-decl nil node_functions_stage nil)
(rcvd_matrix type-eq-decl nil node_functions nil)
(rcvd_matrix_stage type-eq-decl nil node_functions_stage nil)
(non_empty_finite_set type-eq-decl nil finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(check_function type-eq-decl nil node_functions nil)
(check_stage type-eq-decl nil node_functions_stage nil)
(T_low type-eq-decl nil sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(sigma def-decl "real" sigma "reals/")
(agreement_propagation formula-decl nil inexact_reduce_stage nil)
(sigma_last formula-decl nil sigma "reals/"))
nil)
(agreement_propagation-2 nil 3397996105
("" (induct "k")
(("1" (skosimp*)
(("1" (expand "sigma") (("1" (propax) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (inst?)
(("2" (inst?)
(("2" (inst?)
(("2" (inst - "epsilon!1" "rcvd!1")
(("2" (assert)
(("2" (prop)
(("1" (hide -5)
(("1" (expand "protocol")
(("1" (expand "enabled_within?")
(("1"
(expand "generalized_majority_imprecision?")
(("1" (inst - "j!1 + j!2")
(("1" (inst - "j!1 + j!2")
(("1"
(inst - "j!1 + j!2")
(("1"
(assert)
(("1"
(expand "v_min")
(("1"
(expand "v_max")
(("1"
(expand "reduce_select")
(("1"
(replace -2 :hide? t)
(("1"
--> --------------------
--> maximum size reached
--> --------------------
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Lebenszyklus
Die hierunter aufgelisteten Ziele sind für diese Firma wichtig
Ziele
Entwicklung einer Software für die statische Quellcodeanalyse
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