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Proof step 9 from proof ordered-postfix (previous step)

a ' + x1 ≠ [] ∧ (a ' + x1).rest ≠ [], ¬ (a ' + x1).rest.first < (a ' + x1).first ∧ ordered≤((a ' + x1).rest), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ ordered≤(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
x ⊒ a ' + x1, ordered≤(x1), ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ x1 = [], ordered≤(x), x1.first < a

Rule argument

Additional information

Used simplifier rules: c-08: ⊦ (a ' + x).first = a; from specification list%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