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Proof step 7 from proof valid-global-sqn-next-max (previous step)

apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), m < # apebs, valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), (¬ m1 < n ⊃ m1 + 1;n) ≤ (valid-sqns(v0, m5, apebs, m) ∪ (valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)) ⊃ {m1} ;∅)).max, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).max < n ⊦ valid-sqns(v0, m5, apebs, m) ∪ {m1} = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), m < # apebs, valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), (¬ m1 < n ⊃ m1 + 1;n) ≤ (valid-sqns(v0, m5, apebs, m) ++ m1).max, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).max < n ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ ∅ ≠ bag ++ n; (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)