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Proof step 3 from proof map-at (previous step)

∀ n, intfun. n < # ints0 → mapFun(intfun, ints0)[n] = intfun(ints0[n]) ∨ ints0 = [], n < #(i + ints0) ⊦ mapFun(intfun, i + ints0)[n] = intfun((i + ints0)[n]), i + ints0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n ≤ # ints0, ∀ n, intfun. n < # ints0 → mapFun(intfun, ints0)[n] = intfun(ints0[n]) ∨ ints0 = [] ⊦ (intfun(i) ' + mapFun(intfun, ints0))[n] = intfun((i ' + ints0)[n])

Rule argument

Additional information

Used simplifier rules: mapFun-rec: ⊦ mapFun(intfun, i ' + ints) = intfun(i) ' + mapFun(intfun, ints);%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%len-02: ⊦ # i ' = 0 +1; from specification list[intlista]%len: ⊦ #(ints + ints0) = # ints + # ints0; from specification list[intlista]%e-01: ⊦ i ' + ints ≠ []; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%c: ⊦ i + ints = i ' + ints; from specification list[intlista]