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Proof step 5 from proof diff-union (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x))
Proof step 7:
∀ z. rmdup(y0) \ z = rmdup(y0 \ z) ⊦ (a ∈ y0 ⊃ rmdup(y0);a ' + rmdup(y0)) \ z = rmdup((a ' + y0) \ z)

Rule argument

spec: list-dup inst: name: rm-ifrec seq: ⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x)) subst: [x, a] → [y0, a] flags: rewrite

Additional information

Used terms: y0, a