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Proof step 16 from proof perm-put-del1 (previous step)

#oc(y[n], y) = m + 1, y[n] ∈ y, n < # y, y[n] ∈ y[n, a] ∨ y[n] ∈ y -1l y[n] ⊦ y = [], #oc(y[n], y[n, a]) = m, y[n] = a

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: ocs-put-02 seq: ⊦ x[m] = a ∧ a ≠ b ∧ m < # x → #oc(a, x[m, b]) = #oc(a, x) -1 subst: [b, m, x, a] → [a, n, y, y[n]] flags: rewrite, current

Additional information

Used simplifier rules: pred-03: ⊦ n -1 = n - 1; from specification nat%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: a, n, y, y[n]