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Proof step 36 from proof diff-union (previous step)

∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ (a ∈ x0 ∨ a ∈ y ⊃ rmdup(x0 + y);a ' + rmdup(x0 + y)) \ z = rmdup((a ' + (x0 \ z)) + (y \ z)), a ∈ z

User applied rule case distinction

And obtained the following new goals

Proof step 37:
a ∈ x0 ∨ a ∈ y, ∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ rmdup(x0 + y) \ z = rmdup((a ' + (x0 \ z)) + (y \ z)), a ∈ z
Proof step 41:
¬(a ∈ x0 ∨ a ∈ y), ∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ (a ' + rmdup(x0 + y)) \ z = rmdup((a ' + (x0 \ z)) + (y \ z)), a ∈ z

Rule argument

pos: right 1

Proof step 36 from proof diff-union (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information