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Proof step 4 from proof le (previous step)

# y < # filter(rmdup(a ' + x0), y), ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ filter(rmdup(a ' + x0), y) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ a ∈ x → rmdup(a ' + x) = rmdup(x)
Proof step 6:
# y < # filter(rmdup(a ' + x0), y), ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ filter(rmdup(a ' + x0), y) = [], a ∈ x0
Proof step 13:
# y < # filter(rmdup(x0), y), a ∈ x0, ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ filter(rmdup(x0), y) = []

Rule argument

spec: list-dup name: rmdup-y seq: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x) subst: [x, a] → [x0, a] flags: <all paths>

Additional information

Used terms: x0, a