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shostak))
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(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)
(= const-decl "[T, T -> boolean]" equalities nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
(double_index_n_bijective 0
(double_index_n_bijective-1 nil 3397620027
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(("" (split)
(("1" (expand "injective?")
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nil))
nil)
("2" (hide -1)
(("2"
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(("1" (split -1)
(("1"
(inst - "x1!1`1" "x2!1`1" "x1!1`2" "x2!1`2")
(("1" (assert) nil nil)) nil)
("2" (propax) nil nil)
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(("3" (assert) nil nil)) nil))
nil))
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("2" (hide 2 3 -1)
(("2" (skosimp)
(("2" (expand "double_index_n")
(("2"
(case "(i0!1 * i0!1 + i0!1 * j0!1 + i0!1 +
(i0!1 * j0!1 + j0!1 * j0!1 + j0!1))
+ 2*j0!1
=
(i1!1 * i1!1 + i1!1 * j1!1 + i1!1 +
(i1!1 * j1!1 + j1!1 * j1!1 + j1!1))
+ 2*j1!1")
(("1" (assert)
(("1" (hide -3)
(("1"
(case "j0!1<=j1!1")
(("1"
(lemma
"sq_lt"
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(("1"
(lemma
"sq_le"
("nna" "j0!1" "nnb" "j1!1"))
(("1"
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(rewrite "sq_rew")
(("1"
(rewrite "sq_rew")
(("1"
(rewrite "sq_rew")
(("1"
(assert)
(("1"
(lemma
"le_times_le_pos"
("nnx"
"2*i0!1"
"y"
"2*i1!1"
"nnz"
"j0!1"
"w"
"j1!1"))
(("1"
(assert)
nil
nil))
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(case "j0!1>j1!1")
(("1"
(hide 1)
(("1"
(name "DJ" "j0!1-j1!1")
(("1"
(case "DJ>=1")
(("1"
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(("1"
(case "DI>=1")
(("1"
(case-replace
"j0!1=DJ+j1!1")
(("1"
(case-replace
"i1!1=DI+i0!1")
(("1"
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(("1"
(hide
-1
-2
-4
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-9)
(("1"
(assert)
(("1"
(lemma
"trich_lt"
("x"
"DJ"
--> --------------------
--> maximum size reached
--> --------------------
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