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Proof step 15 from proof ole-last (previous step)

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 cut applied rule cut formula

And obtained the following new goals

Proof step 16:
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
Proof step 21:
x0 + a ' = a1 ' + y, a ∈ y, ordered≤(a1 ' + y), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a), a1 ∈ x0 ∨ a1 = a ⊦ a1 = a, b < a1, a < a0, a1 < a0, ordered≤((a0 ' + x0) + a ' + b '), b < a, a < a1, b < a0

Rule argument

fma: a1 = a

Additional information

Used formulas: a1 = a