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Proof step 25 from proof diff-union (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x))
Proof step 27:
∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ (a ∈ x0 + y ⊃ rmdup(x0 + y);a ' + rmdup(x0 + y)) \ z = rmdup(((a ' + x0) \ z) + (y \ z))

Rule argument

spec: list-dup inst: name: rm-ifrec seq: ⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x)) subst: [x, a] → [x0 + y, a] flags: rewrite

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x0 + y, a