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Proof step 7 from proof ordered-postfix (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
x ⊒ a ' ⊦ ordered≤(x)

Rule argument

Additional information

Used simplifier rules: le-o: ⊦ ordered≤(a ');%le-e: ⊦ ordered≤([]);% ⊦ x ⊒ [] ↔ x = []; (s)% ⊦ x + [] = x; (s)% ⊦ (a ' + x).tail = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x ≠ []; (s)