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Proof step 9 from proof valid-eraseq-stronger-prev-append-lref (previous step)

subarray(apebs, 0, m + 1)[m0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), 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, apebs[m0]) ⊦ valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)) ∧ avhdr0.sqn ≠ avhdr.sqn

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ n0 < n → subarray(apebs, m, n)[n0] = apebs[m + n0]
Proof step 11:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[0 + m0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m0 + 1 < # apebs, m < # apebs, m0 < m, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < # apebs, m0 < m + 1, valid-peb(v, n, apebs[m0]), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊦ valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)) ∧ avhdr0.sqn ≠ avhdr.sqn

Rule argument

spec: array-copy, inst: apebs name: subarray-at seq: ⊦ n0 < n → subarray(apebs, m, n)[n0] = apebs[m + n0] subst: [n0, n, m, apebs] → [m0, m + 1, 0, apebs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m < n → ¬ n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%# apebs = n ⊦ subarray(apebs, 0, n) = apebs; (s) Used terms: m0, m + 1, 0, apebs