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Proof step 12 from proof valid-eraseq-stronger-prev-append-lref (previous step)

avhdr0.sqn = avhdr.sqn, apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m0 < # apebs, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < m, m < # apebs, m0 + 1 < # apebs, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)) ⊦

User applied rule apply lemma

And obtained the following new goals

Proof step 13:
⊦ n < m0 ∧ m0 ≤ # apebs ∧ valid-peb(v, m, apebs[n]) → (∃ bag. valid-sqns(v, m, apebs, m0) = bag ++ apebs[n].vidhdr.sqn)
Proof step 14:
avhdr0.sqn = avhdr.sqn, apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 + 1 < # apebs, m < # apebs, m0 < m, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < # apebs, valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), m0 < m ∧ m ≤ # apebs ∧ valid-peb(v, n, apebs[m0]) → (∃ bag. valid-sqns(v, n, apebs, m) = bag ++ apebs[m0].vidhdr.sqn) ⊦

Rule argument

spec: sqns name: valid-sqns-extract-sqn-h seq: ⊦ n < m0 ∧ m0 ≤ # apebs ∧ valid-peb(v, m, apebs[n]) → (∃ bag. valid-sqns(v, m, apebs, m0) = bag ++ apebs[n].vidhdr.sqn) subst: [n, m0, apebs, v, m] → [m0, m, apebs, v, n]

Additional information

Used terms: m0, m, apebs, v, n