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Proof step 48 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m5, apebs).max, apebs[n] = mkpeb(aechdr(m4), avhdr1, buf2, m6, false), wlar[n] = wl-entry(m4, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[m] = wl-entry(m2, used), n < # wlar, m < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(v, m5, mkpeb(aechdr(m4), avhdr1, buf2, m6, false)) ⊦ avhdr1.sqn = valid-sqns(v, m5, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max, n = m

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: sqns name: valid-sqns-write seq: ⊦ n < # apebs → valid-sqns(v, m, apebs[n, apeb]) = ( valid-sqns(v, m, apebs) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅) subst: [apeb, n, apebs, m, v] → [mkpeb(aehdr, avhdr, buf1, m1, boolvar1), m, apebs, m5, v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat[encoding-nat]%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat[encoding-nat]% ⊦ ¬ n < n; (s) Used terms: mkpeb(aehdr, avhdr, buf1, m1, boolvar1), m, apebs, m5, v