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Proof step 42 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf2, m6, stat = erroneous), apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n] = mkpeb(aehdr0, avhdr0, buf, m3, boolvar), wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[n] = wl-entry(m4, stat), n = m, m < # wlar, n < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), stat = used → valid-peb(v, m5, mkpeb(aehdr1, avhdr1, buf2, m6, false)) ∧ avhdr1.sqn = valid-sqns(v, m5, apebs).max, stat ≠ erroneous ∧ stat ≠ erasing → aehdr1 = aechdr(m4), stat = free → avhdr1 = empty ⊦ (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m4)) ∧ ( stat = used → (∃ v, m5. valid-peb(v, m5, mkpeb(aehdr0, avhdr0, buf, m3, false)) ∧ avhdr0.sqn = valid-sqns(v, m5, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m5, apebs).max, apebs[m] = mkpeb(aechdr(m4), avhdr1, buf2, m6, false), wlar[m] = wl-entry(m4, used), m < # wlar, valid-peb(v, m5, mkpeb(aechdr(m4), avhdr1, buf2, m6, false)), valid-peb(mkpeb(aechdr(m4), avhdr1, buf2, m6, false)), valid-peb(mkpeb(aechdr(m4), avhdr1, buf, m3, false)) ⊦ ∃ v, m5. valid-peb(v, m5, mkpeb(aechdr(m4), avhdr1, buf, m3, false)) ∧ avhdr1.sqn = valid-sqns(v, m5, apebs[m, mkpeb(aechdr(m4), avhdr1, buf, m3, false)]).max

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ free; (s)% ⊦ used ≠ erasing; (s)% ⊦ used ≠ erroneous; (s)% ⊦ valid-peb(mkpeb(aehdr, avhdr, buf, m, true)) ↔ false; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)