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Proof step 4 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 5:
⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest))
Proof step 6:
¬(a ' + x1 ≠ [] ∧ (a ' + x1).rest ≠ []), ordered≤(a ' + x1), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ ordered≤(x)
Proof step 9:
a ' + x1 ≠ [] ∧ (a ' + x1).rest ≠ [], ¬ (a ' + x1).rest.first < (a ' + x1).first ∧ ordered≤((a ' + x1).rest), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ ordered≤(x)

Rule argument

spec: inst: name: ole-rec seq: ⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest)) subst: [x] → [a ' + x1] flags: rewrite, current

Additional information

Used terms: a ' + x1