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Proof step 17 from proof ole-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest))
Proof step 19:
(a0 ' + x0) + a ' + b ' ≠ [] ∧ ((a0 ' + x0) + a ' + b ').rest ≠ [], x0 + a ' = a ' + y, ordered≤(a ' + y), a ∈ y, ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a0, ¬ ((a0 ' + x0) + a ' + b ').rest.first < ((a0 ' + x0) + a ' + b ').first ∧ ordered≤(((a0 ' + x0) + a ' + b ').rest), a < a0, b < 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) + a ' + b '] 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 ' + b '