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Proof step 6 from proof perm-dups (previous step)

∃ a, x0, y0, z. y = x0 + (a + (y0 + (a + z))), x ⊆m y, ∀ a. #oc(a, y) ≤ #oc(a, x) ⊦ dups(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
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)

Rule argument

Additional information

Used simplifier rules: ocappend: ⊦ #oc(a, x + y) = #oc(a, x) + #oc(a, y);%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list