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Proof step 3 from proof valid-global-sqn-next-max (previous step)

apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), m < # apebs, valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), max(n, m1 + 1) ≤ (valid-sqns(v0, m5, apebs, m) ∪ (valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)) ⊃ {m1} ;∅)).max, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).max < n ⊦ valid-sqns(v0, m5, apebs, m) ∪ (valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)) ⊃ {m1} ;∅) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ max(n, m) = (n < m ⊃ m;n)
Proof step 5:
apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), m < # apebs, valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), (n < m1 + 1 ⊃ m1 + 1;n) ≤ (valid-sqns(v0, m5, apebs, m) ∪ (valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)) ⊃ {m1} ;∅)).max, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).max < n ⊦ valid-sqns(v0, m5, apebs, m) ∪ (valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)) ⊃ {m1} ;∅) = ∅

Rule argument

spec: min-max name: max seq: ⊦ max(n, m) = (n < m ⊃ m;n) subst: [m, n] → [m1 + 1, n] flags: <all paths>

Additional information

Used terms: m1 + 1, n