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Proof step 4 from proof ocnodups (previous step)

n ≤ #oc(a, a0 ') + #oc(a, x0), ∀ n0, a1. n0 ≤ #oc(a1, x0) → n0 = 0 ∨ n0 = 1 ⊦ n = 0, n = 1, a0 ∈ x0, dups(x0)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 5:
n ≤ #oc(a, a0 ') + #oc(a, x0), ∀ n0, a1. n0 ≤ #oc(a1, x0) → n0 = 0 ∨ n0 = 1 ⊦ a0 = a, n = 0, n = 1, a0 ∈ x0, dups(x0)

Rule argument

fma: a0 = a

Additional information

Used simplifier rules: one: ⊦ #oc(a, a ') = 1;%notin: ⊦ ¬ a ∈ x → #oc(a, x) = 0;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%one-02: ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1); from specification nat Used formulas: a0 = a