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Proof step 2 from proof perm-rmdup-rev (previous step)

∀ y. perm(x0, rmdup(rev(y))) ↔ perm(x0, rmdup(y)) ⊦ perm(a + x0, rmdup(rev(y))) ↔ perm(a + x0, rmdup(y))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
a ∈ y, ∀ y. perm(x0, rmdup(rev(y))) ↔ perm(x0, rmdup(y)) ⊦ perm(x0, rmdup(rev(y)) -1l a) ↔ perm(x0, rmdup(y) -1l a)

Rule argument

Additional information

Used simplifier rules: del-01: ⊦ perm(a ' + x, y) ↔ ¬ ¬(a ∈ y ∧ perm(x, y -1l a));%a: ⊦ (x + y) + z = x + y + z; from specification list%rev-in: ⊦ a ∈ rev(x) ↔ a ∈ x; from specification list-last%rm-in-02: ⊦ a ∈ rmdup(x) ↔ a ∈ x; from specification list-dup%c: ⊦ a + x = a ' + x; from specification list