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Proof step 7 from proof in-prefixn-pos-smaller0 (conclusion)

⊦ a ∈ prefixn(n, x) ∧ m ≤ pos(a, x) → m ≤ n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ prefixn(n, x) = (n ≤ # x ⊃ firstn(n, x);x)

Rule argument

Additional information

[Concretesimprules((Csimpnamedseq(prefixn,,, ⊦ prefixn(n, x) = (n ≤ # x ⊃ firstn(n, x);x)) Csimpnamedseq(list-del,,len-01, ⊦ ¬ # x < pos(a, x)) Csimpnamedseq(nat-basic2,,succ, ⊦ m +1 = m + 1) Csimpnamedforward(nat-basic1,,trans-1, ⊦ n < n0 ∧ n0 < n1 → n < n1) Csimpnamedforward(nat-basic1,,lf, ⊦ m < n ∧ n < n0 → m +1 < n0) Csimpnamedforward(nat-basic1,,f, ⊦ m < n → n ≠ 0) Csimpnamedforward(nat,,fle, ⊦ m < n ∧ n ≤ n0 → m < n0) Csimpnamedseq(nat,,lels-01, ⊦ ¬ m ≤ n ↔ n < m)))]