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Proof step 10 from proof diff-twice-union (previous step)

∀ y, z. (x0 \ y) \ z = x0 \ rmdup(y + z) ⊦ (a ' + (x0 \ y)) \ z = (a ' + x0) \ rmdup(y + z), a ∈ y

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 11:
a ∈ z, ∀ y, z. (x0 \ y) \ z = x0 \ rmdup(y + z) ⊦ (a ' + (x0 \ y)) \ z = (a ' + x0) \ rmdup(y + z), a ∈ y
Proof step 15:
∀ y, z. (x0 \ y) \ z = x0 \ rmdup(y + z) ⊦ a ∈ z, (a ' + (x0 \ y)) \ z = (a ' + x0) \ rmdup(y + z), a ∈ y

Rule argument

fma: a ∈ z

Additional information

Used formulas: a ∈ z