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Proof step 16 from proof ole-last (previous step)

a1 = a, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
x0 + a ' = a ' + y, ordered≤(a ' + y), a ∈ y, ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a0, ordered≤((a0 ' + x0) + a ' + b '), a < a0, b < a

Rule argument

Additional information

Used simplifier rules: ole-in: ⊦ ordered≤(a ' + x) ∧ b ∈ x → ¬ b < a;%in-17: ⊦ a ∈ b ' ↔ a = b; from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%in-12: ⊦ a ∈ y → a ∈ x + y; from specification list%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%irreflexivity: ⊦ ¬ a < a; from specification oelem