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Proof step 32 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].bad) ∧ (wlar[n].status = free → apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[n].status = used → (∃ v, m0. valid-peb(v, m0, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n]) ∧ apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].vidhdr.sqn = valid-sqns(v, m0, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# apebs = # wlar, wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # wlar, n < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ (wlar[n].status = erroneous ↔ apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].bad) ∧ (wlar[n].status = free → apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[n].status = used → (∃ v, m0. valid-peb(v, m0, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n]) ∧ apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n].vidhdr.sqn = valid-sqns(v, m0, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max))

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic[encoding-nat]