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Proof step 10 from proof ordered-postfix (previous step)

ordered≤((a ' + x1).tail), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ a ' + x1 = [], (a ' + x1).tail = [], (a ' + x1).tail.head < (a ' + x1).head, ordered≤(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
ordered≤(x1), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ x1 = [], x1.head < a, ordered≤(x)

Rule argument

Additional information

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