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Proof step 14 from proof ole-last (previous step)

a ∈ y, x0 + a ' = a1 ' + y, ordered≤(a1 ' + y), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a), a = a1 ∨ a ∈ y, a1 ∈ x0 ∨ a1 = a ⊦ a1 < a0, ordered≤((a0 ' + x0) + a ' + b '), b < a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
x0 + a ' = a1 ' + y, a ∈ y, ordered≤(a1 ' + y), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a), a1 ∈ x0 ∨ a1 = a ⊦ b < a1, a < a0, a1 < a0, ordered≤((a0 ' + x0) + a ' + b '), b < a, a < a1, b < a0

Rule argument

Additional information

Used simplifier rules: ole-in: ⊦ ordered≤(a ' + x) ∧ b ∈ x → ¬ b < a;%nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem%a: ⊦ (x + y) + z = x + y + z; from specification list