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

n ≤ # ints0, ∀ n, intfun. n < # ints0 → mapFun(intfun, ints0)[n] = intfun(ints0[n]) ∨ ints0 = [] ⊦ n = 0, mapFun(intfun, ints0)[n - 1] = intfun((i ' + ints0)[n])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
n = m + 1, n ≤ # ints0, ∀ n, intfun. n < # ints0 → mapFun(intfun, ints0)[n] = intfun(ints0[n]) ∨ ints0 = [] ⊦ n = 0, mapFun(intfun, ints0)[m] = intfun((i ' + ints0)[n])

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