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Proof step 33 from proof max-ins-max (previous step)

∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ max(a ' + a0 ' + x0) = a, a0 < a, a < max(a0 ' + x0), a0 < max(a0 ' + x0), ordered≤(a0 ' + x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ x ≠ [] → max(a ' + x) = (max(x) < a ⊃ a;max(x))
Proof step 35:
∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ a0 ' + x0 = [], (max(a0 ' + x0) < a ⊃ a;max(a0 ' + x0)) = a, a0 < max(a0 ' + x0), a < max(a0 ' + x0), a0 < a, ordered≤(a0 ' + x0)

Rule argument

spec: <toplevel> name: max-rec seq: ⊦ x ≠ [] → max(a ' + x) = (max(x) < a ⊃ a;max(x)) subst: [x, a] → [a0 ' + x0, a] flags: <all paths>

Additional information

Used simplifier rules: ⊦ x + y = [] ↔ x = [] ∧ y = []; (as)% ⊦ a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a0 ' + x0, a