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Proof step 4 from proof rm-size-in-01 (previous step)

∀ a. a ∈ rmdup(x + y + z) → a ∈ rmdup(x + z), # rmdup(x + y + z) = # rmdup(x + z), a ∈ y ⊦ a ∈ x, a ∈ z

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 1 terms: a

Additional information

Used simplifier rules: rm-in-02: ⊦ a ∈ rmdup(x) ↔ a ∈ x;%rm-in: ⊦ a ∈ rmdup(x + y) ↔ a ∈ x ∨ a ∈ y;%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%in-11: ⊦ a ∈ x → a ∈ x + y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a