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Proof step 4 from proof app (previous step)

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

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 ' + x0 ≠ [] ∧ (a ' + x0).rest ≠ [], ordered≤((a ' + x0) + y), (∃ y. ordered≤(x0 + y)) → ordered≤(x0) ⊦ ¬ (a ' + x0).rest.first < (a ' + x0).first ∧ ordered≤((a ' + x0).rest)

Rule argument

spec: olist inst: name: ole-rec seq: ⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest)) subst: [x] → [a ' + x0] flags: rewrite, current

Additional information

Used simplifier rules: le-o: ⊦ ordered≤(a ');%e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list%Nil: ⊦ [] + x = x; from specification list%app: ⊦ x + [] = x; from specification list Used terms: a ' + x0