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Proof step 16 from proof splice-resize-less (previous step)

n2 = 0, n < n2 + n1, n2 ≤ m0 ⊦ (# splice(ar0, n0, ar1, n1, m0) ≤ n ⊃ zero;splice(ar0, n0, ar1, n1, m0)[n]) = (# splice(ar0, n0, ar1, n1, n2) ≤ n ⊃ zero;splice(ar0, n0, ar1, n1, n2)[n]), m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
⊦ splice(ar0, n0, ar1, n1, 0) = ar1
Proof step 18:
n < n1 ⊦ (# splice(ar0, n0, ar1, n1, m0) ≤ n ⊃ zero;splice(ar0, n0, ar1, n1, m0)[n]) = (# ar1 ≤ n ⊃ zero;ar1[n])

Rule argument

Additional information

Used simplifier rules: splice-0: ⊦ splice(ar0, n0, ar1, n1, 0) = ar1;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ 0 ≤ m; (s)