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Proof step 25 from proof valid-sqns-write-h (previous step)

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

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 4 flags: discard

Additional information

Used simplifier rules: valid-peb-in-sqnums-h: n0 < n1, n1 ≤ # apebs ⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ∧ apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar) → avhdr.sqn ∈ valid-sqns(v, m, apebs, n1);% ⊦ (bag -- n) ++ n = (n ∈ bag ⊃ bag;bag ++ n); (s)% ⊦ m < n → m ≤ n; (s)