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Proof step 20 from proof range-eq-resize (previous step)

m + n1 ≤ # ar1, m + n1 ≤ n, n ≤ # ar1, n0 + m ≤ # ar0, n1 + m ≤ # ar1, ∀ n. n < m → ar0[n0 + n] = ar1[n1 + n] ⊦ n0 + m ≤ # ar0 ∧ n1 + m ≤ # resize(ar1, n) ∧ (∀ n2. n2 < m → ar0[n0 + n2] = resize(ar1, n)[n1 + n2])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
⊦ # resize(ar, n) = n
Proof step 22:
n2 < m, m + n1 ≤ # ar1, m + n1 ≤ n, n ≤ # ar1, n0 + m ≤ # ar0, n1 + m ≤ # ar1, ∀ n. n < m → ar0[n0 + n] = ar1[n1 + n] ⊦ ar0[n0 + n2] = resize(ar1, n)[n1 + n2]

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%c: ⊦ m + n = n + m; from specification nat-basic