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

x ⊆m x0 + a ' + y0 + a ' + z, ∀ a0. #oc(a0, x0) + #oc(a0, a ') + #oc(a0, y0) + #oc(a0, a ') + #oc(a0, z) ≤ #oc(a0, x) ⊦ dups(x)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: a

Additional information

Used simplifier rules: one: ⊦ #oc(a, a ') = 1;%ocnodups: ⊦ n ≤ #oc(a, x) ∧ ¬ dups(x) → n ≤ 1;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%le-num-06: n0 < n ⊦ ¬ m + (* n) ≤ (* n0); from specification nat Used terms: a