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

apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), n ≤ avhdr.sqn, ∀ v, m0. valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅) ≠ ∅ → (valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅)).max < n, ∀ v, m0. valid-sqns(v, m0, apebs, m) ≠ ∅ → valid-sqns(v, m0, apebs, m).max < n ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ valid-peb(apeb) ↔ (∃ v, m. valid-peb(v, m, apeb))
Proof step 9:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, n ≤ avhdr.sqn, ∀ v, m0. valid-sqns(v, m0, apebs, m) ≠ ∅ → valid-sqns(v, m0, apebs, m).max < n, ∀ v, m0. valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅) ≠ ∅ → (valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅)).max < n, ∃ v, m. valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊦

Rule argument

spec: valid-peb name: valid-peb0 seq: ⊦ valid-peb(apeb) ↔ (∃ v, m. valid-peb(v, m, apeb)) subst: [apeb] → [mkpeb(aehdr, avhdr, buf, m1, boolvar)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, buf, m1, boolvar)