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Proof step 11 from proof ole-last (previous step)

ordered≤(((a0 ' + x0) + a ').tail), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ (a0 ' + x0) + a ' = [], ((a0 ' + x0) + a ').tail = [], b < a, ((a0 ' + x0) + a ').tail.head < ((a0 ' + x0) + a ').head, ordered≤((a0 ' + x0) + a ' + b ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
ordered≤(x0 + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a, (x0 + a ').head < a0, ordered≤((a0 ' + x0) + a ' + b ')

Rule argument

Additional information

Used simplifier rules: ⊦ (a ' + x).head = a; (s)% ⊦ a ' + x ≠ []; (s)% ⊦ x + a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (a ' + x).tail = x; (s)