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Proof step 39 from proof rm-allsize (previous step)

rmdup(z) = y + a ' + z0, a ∈ z, a0 ∈ y ∨ a0 ∈ z0 ⊦ # rmdup(x0) = # rmdup((y0 + y) + z0), a0 ∈ x0, a ∈ y0, a ∈ x0, a ∈ y, a ∈ z0, a0 ∈ z, a0 ∈ y0

User applied rule cut formula

And obtained the following new goals

Proof step 40:
rmdup(z) = y + a ' + z0, a ∈ z, a0 ∈ y ∨ a0 ∈ z0 ⊦ a0 ∈ rmdup(z), # rmdup(x0) = # rmdup((y0 + y) + z0), a0 ∈ x0, a ∈ y0, a ∈ x0, a ∈ y, a ∈ z0, a0 ∈ z, a0 ∈ y0

Rule argument

fma: a0 ∈ rmdup(z)

Additional information

Used simplifier rules: rm-in-02: ⊦ a ∈ rmdup(x) ↔ a ∈ x; Used formulas: a0 ∈ rmdup(z)