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Proof step 17 from proof valid-eraseqp-invalidate (previous step)

apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m, apeb][m0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m0 = m, m < # apebs, m0 < # apebs, valid-eraseq(apebs, q0), ∀ m, apebs, apeb. m < # apebs ∧ valid-eraseq(apebs, q0) → valid-eraseq(apebs[m, apeb], q0) ∨ valid-peb(apeb) ⊦ valid-peb(apeb), (valid-peb(mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)) → avhdr.vol × avhdr.leb = avhdr0.vol × avhdr0.leb) ∧ valid-eraseq(apebs[m, apeb], q0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, valid-eraseq(apebs, q0), ∀ m, apebs, apeb. m < # apebs ∧ valid-eraseq(apebs, q0) → valid-eraseq(apebs[m, apeb], q0) ∨ valid-peb(apeb) ⊦ valid-eraseq(apebs[m, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)], q0), valid-peb(mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0))

Rule argument

Additional information

Used simplifier rules: ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)