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Proof step 4 from proof del1-01 (previous step)

∀ y, a. filter(rmdup(x0), y -1l a) = filter(rmdup(x0), y) ∨ a ∈ x0 ⊦ filter(rmdup(a0 ' + x0), y -1l a) = filter(rmdup(a0 ' + x0), y), a = a0, a ∈ x0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x))
Proof step 6:
∀ y, a. filter(rmdup(x0), y -1l a) = filter(rmdup(x0), y) ∨ a ∈ x0 ⊦ filter((a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)), y -1l a) = filter((a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)), y), a = a0, a ∈ x0

Rule argument

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

Additional information

Used terms: x0, a0