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Proof step 4 from proof mklist-rmdup (previous step)

∀ a, n. rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ n = 0 ∨ a ∈ x0 ⊦ n = 0, rmdup((a0 ' + x0) + mklist(a, n)) = rmdup(a0 ' + x0) + a ', 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:
∀ a, n. rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ n = 0 ∨ a ∈ x0 ⊦ n = 0, (a0 ∈ x0 + mklist(a, n) ⊃ rmdup(x0 + mklist(a, n));a0 ' + rmdup(x0 + mklist(a, n))) = rmdup(a0 ' + x0) + a ', 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 + mklist(a, n), a0] flags: rewrite

Additional information

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