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Proof step 7 from proof diff-union (previous step)

∀ z. rmdup(y0) \ z = rmdup(y0 \ z) ⊦ (a ∈ y0 ⊃ rmdup(y0);a ' + rmdup(y0)) \ z = rmdup((a ' + y0) \ z)

User applied rule case distinction

And obtained the following new goals

Proof step 8:
a ∈ y0, ∀ z. rmdup(y0) \ z = rmdup(y0 \ z) ⊦ rmdup(y0) \ z = rmdup((a ' + y0) \ z)
Proof step 14:
∀ z. rmdup(y0) \ z = rmdup(y0 \ z) ⊦ (a ' + rmdup(y0)) \ z = rmdup((a ' + y0) \ z), a ∈ y0

Rule argument

pos: right 1

Additional information