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Proof step 8 from proof rmdup-last (previous step)

∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ a = a0, rmdup((a0 ' + x0) + a ') = (a0 ' + rmdup(x0)) + a ', a0 ∈ x0, a ∈ x0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x))
Proof step 10:
∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ a = a0, (a0 ∈ x0 + a ' ⊃ rmdup(x0 + a ');a0 ' + rmdup(x0 + a ')) = (a0 ' + rmdup(x0)) + a ', a0 ∈ x0, a ∈ x0

Rule argument

spec: inst: name: rm-ifrec seq: ⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x)) subst: [x, a] → [x0 + a ', a0] flags: rewrite, current

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x0 + a ', a0