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Proof step 12 from proof del1-01 (previous step)

ordered≤(a2 ' + y), ∀ a1. ordered≤((a2 ' + y) -1l a1) ⊦ a = a0, ordered≤(a0 ' + ((a2 ' + y) -1l a)), a2 < a0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest))
Proof step 14:
a0 ' + ((a2 ' + y) -1l a) ≠ [] ∧ (a0 ' + ((a2 ' + y) -1l a)).rest ≠ [], ordered≤(a2 ' + y), ∀ a1. ordered≤((a2 ' + y) -1l a1) ⊦ a = a0, ¬ (a0 ' + ((a2 ' + y) -1l a)).rest.first < (a0 ' + ((a2 ' + y) -1l a)).first ∧ ordered≤((a0 ' + ((a2 ' + y) -1l a)).rest), a2 < a0

Rule argument

spec: inst: name: ole-rec seq: ⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest)) subst: [x] → [a0 ' + ((a2 ' + y) -1l a)] 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 Used terms: a0 ' + ((a2 ' + y) -1l a)