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Proof step 13 from proof rm-size-01 (previous step)

a ∈ x0, ∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ # (a0 ∈ x0 ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # rmdup((a0 ' + x0) + y), a0 ∈ y

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 14:
a0 ∈ x0, a ∈ x0, ∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ # (a0 ∈ x0 ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # rmdup((a0 ' + x0) + y), a0 ∈ y
Proof step 16:
a ∈ x0, ∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ a0 ∈ x0, # (a0 ∈ x0 ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # rmdup((a0 ' + x0) + y), a0 ∈ y

Rule argument

fma: a0 ∈ x0

Additional information

Used formulas: a0 ∈ x0