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Proof step 7 from proof size-perm (previous step)

# x = # y, ∀ a. a ∈ y → a ∈ x, ∀ a. a ∈ x → a ∈ y ⊦ #oc(a, x) ≤ #oc(a, y), dups(x), dups(y)

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: a

Additional information

Used simplifier rules: oc-dups: ⊦ n < #oc(a, x) ∧ ¬ dups(x) → #oc(a, x) = 1;%oc-zero: ⊦ #oc(a, x) = 0 ↔ ¬ a ∈ x;%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1 Used terms: a