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Proof step 4 from proof ordered-prefix (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ a ' + x ⊑ y ↔ y ≠ [] ∧ a = y.first ∧ x ⊑ y.rest
Proof step 6:
ordered≤(x0), x0 ≠ [] ∧ a = x0.first ∧ x1 ⊑ x0.rest, (∃ x0. x1 ⊑ x0 ∧ ordered≤(x0)) → ordered≤(x1) ⊦ ordered≤(a ' + x1)

Rule argument

spec: list-last inst: name: prefix-rec-01 seq: ⊦ a ' + x ⊑ y ↔ y ≠ [] ∧ a = y.first ∧ x ⊑ y.rest subst: [y, x, a] → [x0, x1, a] flags: rewrite

Additional information

Used terms: x0, x1, a