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Proof step 7 from proof pos-at (previous step)

n ≤ # str0, ∀ n0. n0 < # str0 → pos(s→l(str0)[n0], str0) = n0 ∨ str0 = "" ⊦ char ' + str0 = "", n = 0, pos(s→l(str0)[n - 1], char ' + str0) = n, dups(s→l(str0)), char ∈ s→l(str0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
n = m + 1, n ≤ # str0, ∀ n0. n0 < # str0 → pos(s→l(str0)[n0], str0) = n0 ∨ str0 = "" ⊦ char ' + str0 = "", n = 0, pos(s→l(str0)[m], char ' + str0) = n, dups(s→l(str0)), char ∈ s→l(str0)

Rule argument

spec: nat inst: name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m] flags:

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m