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Proof step 10 from proof ole-last (previous step)

(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 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
ordered≤(x0 + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a, ordered≤((a0 ' + x0) + a ' + b '), (x0 + a ').first < a0

Rule argument

Additional information

Used simplifier rules: c-08: ⊦ (a ' + x).first = a; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%e-02: ⊦ x + a ' ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list