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Proof step 12 from proof ocs-put-02 (previous step)

m1 < # x0, m1 < # x0 → #oc(x0[m1], x0[m1, b]) = #oc(x0[m1], x0) - 1 ∨ x0[m1] = b, ∀ m0, b0. m0 < # x0 → #oc(x0[m0], x0[m0, b0]) = #oc(x0[m0], x0) - 1 ∨ x0[m0] = b0 ⊦ 1 + #oc(x0[m1], x0[m1, b]) = #oc(x0[m1], x0), x0[m1] = b, x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
#oc(x0[m1], x0[m1, b]) = #oc(x0[m1], x0) - 1, m1 < # x0, ∀ m0, b0. m0 < # x0 → #oc(x0[m0], x0[m0, b0]) = #oc(x0[m0], x0) - 1 ∨ x0[m0] = b0 ⊦ 1 + #oc(x0[m1], x0[m1, b]) = #oc(x0[m1], x0), x0[m1] = b, x0 = []

Proof step 12 from proof ocs-put-02 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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