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Proof step 5 from proof ole-01 (previous step)

a0 < a, ∀ a. ordered≤(ins≤(a, x0)) ↔ ordered≤(x0) ⊦ ordered≤(a0 ' + ins≤(a, x0)) ↔ ordered≤(a0 ' + x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest))
Proof step 7:
a0 ' + ins≤(a, x0) ≠ [] ∧ (a0 ' + ins≤(a, x0)).rest ≠ [], a0 < a, ∀ a. ordered≤(ins≤(a, x0)) ↔ ordered≤(x0) ⊦ ¬ (a0 ' + ins≤(a, x0)).rest.first < (a0 ' + ins≤(a, x0)).first ∧ ordered≤((a0 ' + ins≤(a, x0)).rest) ↔ ordered≤(a0 ' + x0)

Rule argument

spec: olist inst: name: ole-rec seq: ⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest)) subst: [x] → [a0 ' + ins≤(a, x0)] flags: rewrite, current

Additional information

Used simplifier rules: empty: ⊦ ins≤(a, x) ≠ [];%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 Used terms: a0 ' + ins≤(a, x0)