sent: VAR sent_vec
rcvd: VAR rcvd_matrix
check: VAR check_function
epsilon: VAR [nat -> nonneg_real]
tau: VAR [i: nat -> tau_type]
cf: VAR [nat -> consensus_function]
% % Abstracted fault assumptions %
% same predicate is in exact_comm
enabled_within?(rcvd, check, j, k)(sources): bool = FORALL i : j <= i AND i < k IMPLIES
enabled_within?[N(i), N(i + 1), real](rcvd(i), check(i))(sources(i))
% (simple) majority
majority_lower?(sent, rcvd, check, epsilon, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
majority_lower?[N(i), N(i + 1)](sent(i), rcvd(i), check(i), epsilon(i))
majority_upper?(sent, rcvd, check, epsilon, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
majority_upper?[N(i), N(i + 1)](sent(i), rcvd(i), check(i), epsilon(i))
majority_imprecision?(sent, rcvd, check, epsilon, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
majority_imprecision?[N(i), N(i + 1)](sent(i), rcvd(i), check(i), epsilon(i))
exists_all_symmetric?(sent, rcvd, check, epsilon, cf, j, k): bool = EXISTS i: j <= i AND i < k AND
inexact_consensus?(cf(i)) AND
all_symmetric?(rcvd(i), check(i), epsilon(i)) AND
majority_imprecision?(sent, rcvd, check, epsilon, i + 1, k)
% quorum, a generalized majority (from simple to consensus to unamimous)
quorum_lower?(sent, rcvd, check, tau, epsilon, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
quorum_lower?[N(i), N(i + 1)](sent(i), rcvd(i), check(i), tau(i), epsilon(i))
quorum_upper?(sent, rcvd, check, tau, epsilon, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
quorum_upper?[N(i), N(i + 1)](sent(i), rcvd(i), check(i), tau(i), epsilon(i))
quorum_imprecision?(sent, rcvd, check, tau, epsilon, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
quorum_imprecision?[N(i), N(i + 1)](sent(i), rcvd(i), check(i), tau(i), epsilon(i))
exists_all_symmetric?(sent, rcvd, check, tau, epsilon, cf, j, k): bool = EXISTS i: j <= i AND i < k AND
inexact_consensus?(cf(i)) AND
all_symmetric?(rcvd(i), check(i), epsilon(i)) AND
quorum_imprecision?(sent, rcvd, check, tau, epsilon, i + 1, k)
END inexact_comm
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