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Proof step 3 from proof ole-last (previous step)

∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a), ordered≤((a0 + x0) + a ') ⊦ ordered≤((a0 + x0) + a ' + b ') ↔ ¬ b < a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
ordered≤((a0 ' + x0) + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ ordered≤((a0 ' + x0) + a ' + b ') ↔ ¬ b < a

Rule argument

Additional information

Used simplifier rules: cons-02: ⊦ ordered≤(a ' + x) → ordered≤(x);%app-01: ⊦ ordered≤(x + y) → ordered≤(y);%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list