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Proof step 12 from proof pos-get (previous step)

m < # x0, ∀ n. n < # x0 → pos(x0[n], x0) = n ⊦ pos(x0[m], x0) + 1 = m + 1, x0[m] = a, x0 = [], dups(x0), a ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
m < # x0, ∀ n. n < # x0 → pos(x0[n], x0) = n ⊦ x0[m] = a, pos(x0[m], x0) = m, x0 = [], dups(x0), a ∈ x0

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)