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Proof step 8 from proof ole-last (previous step)

ordered≤((a0 ' + x0) + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a, ordered≤((a0 ' + x0) + a ' + b ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest))
Proof step 10:
(a0 ' + x0) + a ' ≠ [] ∧ ((a0 ' + x0) + a ').rest ≠ [], ¬ ((a0 ' + x0) + a ').rest.first < ((a0 ' + x0) + a ').first ∧ ordered≤(((a0 ' + x0) + a ').rest), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a, ordered≤((a0 ' + x0) + a ' + b ')

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) + a '] flags: rewrite, current

Additional information

Used simplifier rules: 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%e-02: ⊦ x + a ' ≠ []; from specification list Used terms: (a0 ' + x0) + a '