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Proof step 19 from proof valid-wl-use (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), n < # wlar, n < # apebs, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)), valid-sqns(v, m, apebs) ≠ ∅ → valid-sqns(v, m, apebs).max < avhdr0.sqn, ∀ m0. m0 < # wlar ∧ m0 ≠ n ∧ wlar[m0].status = used → apebs[m0].vidhdr.vol ≠ v ∨ apebs[m0].vidhdr.leb ≠ m, ∀ 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)) ⊦ avhdr0.sqn = ( (valid-sqns(v, m, apebs) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)) ⊃ {mkpeb(aehdr0, avhdr0, buf0, m1, false).vidhdr.sqn} ;∅) ).max

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), avhdr0.sqn < (valid-sqns(v, m, apebs) \ (valid-peb(v, m, mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1)) ⊃ {avhdr1.sqn} ;∅)).max, n < # wlar, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)), valid-sqns(v, m, apebs) ≠ ∅ → valid-sqns(v, m, apebs).max < avhdr0.sqn, ∀ 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)), ∀ m0. m0 < # wlar ∧ m0 ≠ n ∧ wlar[m0].status = used → apebs[m0].vidhdr.vol ≠ v ∨ apebs[m0].vidhdr.leb ≠ m ⊦ valid-sqns(v, m, apebs) \ (valid-peb(v, m, mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1)) ⊃ {avhdr1.sqn} ;∅) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m = (bag ++ m).max ↔ ¬(bag ≠ ∅ ∧ m < bag.max); (s)%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]% ⊦ bag ∪ {n} = bag ++ n; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)