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Proof step 17 from proof ole-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
x0 + a ' = a ' + y, ordered≤(a ' + y), a ∈ y, ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a0, a < a0, b < a, ordered≤((a0 ' + x0) + a ' + b ')

Rule argument

Additional information

Used simplifier rules: ole-in: ⊦ ordered≤(a ' + x) ∧ b ∈ x → ¬ b < a;% ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)% ⊦ a ∈ y → a ∈ x + y; (s)%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list% ⊦ ¬ a < a; (s)