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Proof step 10 from proof rm-size-02 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 11:
a0 ∈ x0 ∨ a0 ∈ y, a ∈ y, ∀ a, y. a ∈ y → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ # rmdup(x0 + a ' + y) = # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + y);a0 ' + rmdup(x0 + y))
Proof step 13:
¬(a0 ∈ x0 ∨ a0 ∈ y), a ∈ y, ∀ a, y. a ∈ y → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ #(a0 ' + rmdup(x0 + a ' + y)) = # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + y);a0 ' + rmdup(x0 + y))

Rule argument

pos: right 1

Proof step 10 from proof rm-size-02 (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information