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Proof step 27 from proof range-eq-splice-less (previous step)

ar2[n2 + n3] = (n1 + n3 < n1 + n4 ∨ (n1 + n4) + m0 ≤ n1 + n3 ⊃ resize(ar0, (n1 + n4) + m0)[n1 + n3];ar[(n1 + n3) + n - n1 + n4]), n3 < m0, n3 < m1, # ar0 < (n1 + n4) + m1, # ar0 < (n1 + n4) + m0, n1 + n3 < # resize(ar0, (n1 + n4) + m0), m1 ≤ m0, n + m0 ≤ # ar, n2 + m1 ≤ # ar2 ⊦ ar2[n2 + n3] = copy(ar, n, resize(ar0, (n1 + n4) + m1), n1 + n4, m1)[n1 + n3]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
⊦ # resize(ar, n) = n
Proof step 29:
ar2[n2 + n3] = (n3 < n4 ⊃ resize(ar0, (n1 + n4) + m0)[n1 + n3];ar[n3 + n - n4]), n3 < n4 + m0, n3 < m0, n3 < m1, # ar0 < (n1 + n4) + m1, # ar0 < (n1 + n4) + m0, m1 ≤ m0, n + m0 ≤ # ar, n2 + m1 ≤ # ar2 ⊦ ar2[n2 + n3] = copy(ar, n, resize(ar0, (n1 + n4) + m1), n1 + n4, m1)[n1 + n3]

Rule argument

Additional information

Used simplifier rules: resize-len: ⊦ # resize(ar, n) = n;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m + n - n + n1 = m - n1; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)