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Proof step 11 from proof rm-rm-02 (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 12:
a ∈ rmdup(y), ∀ y. rmdup(x0 + rmdup(y)) = rmdup(x0 + y), a ∈ x0 ∨ a ∈ y ⊦ rmdup(x0 + rmdup(y)) = rmdup((a ' + x0) + y)
Proof step 14:
∀ y. rmdup(x0 + rmdup(y)) = rmdup(x0 + y), a ∈ x0 ∨ a ∈ y ⊦ a ∈ rmdup(y), rmdup(x0 + rmdup(y)) = rmdup((a ' + x0) + y)

Rule argument

fma: a ∈ rmdup(y)

Additional information

Used formulas: a ∈ rmdup(y)