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Proof step 4 from proof ins-max (previous step)

ordered≤(a0 ' + x), ∀ a1. ins≤(a1, x) = x + a1 ' ∨ a1 < max(x) ⊦ ins≤(a, a0 ' + x) = (a0 ' + x) + a ', a < max(a0 ' + x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ordered≤(a ' + x) → ins≤(a, x) = a ' + x
Proof step 6:
¬ ordered≤(a ' + a0 ' + x), ordered≤(a0 ' + x), ∀ a1. ins≤(a1, x) = x + a1 ' ∨ a1 < max(x) ⊦ ins≤(a, a0 ' + x) = (a0 ' + x) + a ', a < max(a0 ' + x)
Proof step 14:
ordered≤(a ' + a0 ' + x), ordered≤(a0 ' + x), ∀ a1. ins≤(a1, x) = x + a1 ' ∨ a1 < max(x) ⊦ a ' + a0 ' + x = (a0 ' + x) + a ', a < max(a0 ' + x)

Rule argument

spec: olist inst: name: cons-03 seq: ⊦ ordered≤(a ' + x) → ins≤(a, x) = a ' + x subst: [x, a] → [a0 ' + x, a] flags: rewrite

Additional information

Used terms: a0 ' + x, a