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Proof step 10 from proof ordered-append (previous step)

ordered≤(a ' + x1), ordered≤(x1 + a0 ' + y), ∀ x. ordered≤(x) ∧ (x ≠ [] → ¬ x.first < x1.last) → ordered≤(x1 + x) ⊦ x1 = [], ordered≤(a ' + x1 + a0 ' + y), a0 < x1.last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.rest.first < y.first ∧ ordered≤(y.rest)
Proof step 12:
ordered≤(a ' + x1), ordered≤(x1 + a0 ' + y), ∀ x. ordered≤(x) ∧ (x ≠ [] → ¬ x.first < x1.last) → ordered≤(x1 + x) ⊦ x1 = [], #(a ' + x1 + a0 ' + y) ≤ 1 ∨ ¬ (a ' + x1 + a0 ' + y).rest.first < (a ' + x1 + a0 ' + y).first ∧ ordered≤((a ' + x1 + a0 ' + y).rest), a0 < x1.last

Rule argument

spec: inst: name: k-le-r seq: ⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.rest.first < y.first ∧ ordered≤(y.rest) subst: [y] → [a ' + x1 + a0 ' + y] flags: rewrite, current

Additional information

Used terms: a ' + x1 + a0 ' + y