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Proof step 5 from proof ordered-prefix (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ a ' + x ⊑ y ↔ y ≠ [] ∧ a = y.head ∧ x ⊑ y.tail
Proof step 7:
a = x0.head, ordered≤(x0), x1 ⊑ x0.tail, (∃ x0. ordered≤(x0) ∧ x1 ⊑ x0) → ordered≤(x1) ⊦ x0 = [], ordered≤(a ' + x1)

Rule argument

spec: list-last name: prefix-rec-01 seq: ⊦ a ' + x ⊑ y ↔ y ≠ [] ∧ a = y.head ∧ x ⊑ y.tail subst: [y, x, a] → [x0, x1, a] flags: <all paths>

Additional information

Used terms: x0, x1, a