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Proof step 9 from proof ordered-prefix (previous step)

ordered≤(a ' + y), x1 ⊑ y, (∃ x0. x1 ⊑ x0 ∧ ordered≤(x0)) → ordered≤(x1) ⊦ ordered≤(a ' + x1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.rest.first < y.first ∧ ordered≤(y.rest)
Proof step 11:
#(a ' + y) ≤ 1 ∨ ¬ (a ' + y).rest.first < (a ' + y).first ∧ ordered≤((a ' + y).rest), x1 ⊑ y, (∃ x0. x1 ⊑ x0 ∧ ordered≤(x0)) → ordered≤(x1) ⊦ ordered≤(a ' + x1)

Rule argument

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

Additional information

Used terms: a ' + y