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Proof step 8 from proof valid-wl-next-bad (previous step)

# apebs = # wlar, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, boolvar), boolvar, m < # wlar, ∀ n. n < m → (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, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max)) ⊦ ∀ n. ¬ m < n → (wlar[m, wl-entry(m0, erroneous)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m0, erroneous)][n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[m, wl-entry(m0, erroneous)][n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[m, wl-entry(m0, erroneous)][n].status = used → (∃ v, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = (valid-sqns(v, m1, apebs, m) ∪ (valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m2, boolvar)) ⊃ {avhdr.sqn} ;∅)).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# apebs = # wlar, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, true), m < # wlar, n < # wlar, n ≤ m, ∀ n. n < m → (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, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max)) ⊦ (wlar[m, wl-entry(m0, erroneous)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m0, erroneous)][n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[m, wl-entry(m0, erroneous)][n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[m, wl-entry(m0, erroneous)][n].status = used → (∃ v, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max))

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]% ⊦ ∅ ∪ bag0 = bag0; (s)% ⊦ ¬ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, true)); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)