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Proof step 2 from proof unique-sqns-write-valid (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊦ unique-sqns(apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]) ↔ unique-sqns(apebs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊦ (∀ v, m0. unique-elems(valid-sqns(v, m0, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]))) ↔ (∀ v, m. unique-elems(valid-sqns(v, m, apebs)))

Rule argument

Additional information

Used simplifier rules: unique-sqns: ⊦ unique-sqns(apebs) ↔ (∀ v, m. unique-elems(valid-sqns(v, m, apebs)));% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic