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

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 17:
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 ')
Proof step 22:
x0 + a ' = a1 ' + y, ordered≤(a1 ' + y), a ∈ y, ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a), a1 ∈ x0 ∨ a1 = a ⊦ a1 = a, b < a0, a < a1, b < a, a1 < a0, a < a0, b < a1, ordered≤((a0 ' + x0) + a ' + b ')

Rule argument

fma: a1 = a

Additional information

Used formulas: a1 = a