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

ordered≤(a ' + x1), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ ordered≤(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ x ≠ [] ∧ x.tail ≠ [] → (ordered≤(x) ↔ ¬ x.tail.head < x.head ∧ ordered≤(x.tail))
Proof step 7:
ordered≤(a ' + x1), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ ordered≤(x), a ' + x1 ≠ [] ∧ (a ' + x1).tail ≠ []
Proof step 10:
ordered≤((a ' + x1).tail), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ a ' + x1 = [], (a ' + x1).tail = [], (a ' + x1).tail.head < (a ' + x1).head, ordered≤(x)

Rule argument

spec: <toplevel> name: ole-rec seq: ⊦ x ≠ [] ∧ x.tail ≠ [] → (ordered≤(x) ↔ ¬ x.tail.head < x.head ∧ ordered≤(x.tail)) subst: [x] → [a ' + x1] flags: <all paths>

Additional information

Used terms: a ' + x1