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Proof step 9 from proof ocs-put-02 (previous step)

m = m1 + 1, (a0 ' + x0)[m] = a0, m ≤ # x0, ∀ m0, b0. x0[m0] ≠ b0 ∧ m0 < # x0 → #oc(x0[m0], x0[m0, b0]) = #oc(x0[m0], x0) - 1 ⊦ m = 0, a0 = b, 1 + #oc(a0, x0[m1, b]) = #oc(a0, x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
m1 < # x0, ∀ m0, b0. x0[m0] ≠ b0 ∧ m0 < # x0 → #oc(x0[m0], x0[m0, b0]) = #oc(x0[m0], x0) - 1 ⊦ 1 + #oc(x0[m1], x0[m1, b]) = #oc(x0[m1], x0), x0[m1] = b, x0 = []

Rule argument

Additional information

Used simplifier rules: l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%succ-01: ⊦ m + 1 ≤ n ↔ m < n; from specification nat%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%get-succ: ⊦ (a ' + x)[n + 1] = x[n]; from specification list-del