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Proof step 4 from proof resize-twice (previous step)

# ar ≤ n ⊦ # resize(resize(ar, n), m) = # resize(ar, m) ∧ (∀ n0. n0 < # resize(resize(ar, n), m) → resize(resize(ar, n), m)[n0] = resize(ar, m)[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ # resize(ar, n) = n
Proof step 6:
⊦ m < n → resize(ar, n)[m] = (# ar ≤ m ∧ m < n ⊃ zero;ar[m])
Proof step 7:
n0 < m, # ar ≤ n ⊦ (n ≤ n0 ⊃ zero;resize(ar, n)[n0]) = (# ar ≤ n0 ⊃ zero;ar[n0])

Rule argument

Additional information

Used simplifier rules: resize-len: ⊦ # resize(ar, n) = n;%resize-at: ⊦ m < n → resize(ar, n)[m] = (# ar ≤ m ∧ m < n ⊃ zero;ar[m]);% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic