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Proof step 7 from proof del1-01 (previous step)

ordered≤(a0 ' + x0), ∀ a1. ordered≤(x0 -1l a1) ⊦ a = a0, ordered≤(a0 ' + (x0 -1l a))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest))
Proof step 9:
a0 ' + x0 ≠ [] ∧ (a0 ' + x0).rest ≠ [], ¬ (a0 ' + x0).rest.first < (a0 ' + x0).first ∧ ordered≤((a0 ' + x0).rest), ∀ a1. ordered≤(x0 -1l a1) ⊦ a = a0, ordered≤(a0 ' + (x0 -1l a))

Rule argument

spec: inst: name: ole-rec seq: ⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest)) subst: [x] → [a0 ' + 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%app: ⊦ x + [] = x; from specification list%del1-e: ⊦ [] -1l a = []; from specification list-del Used terms: a0 ' + x0