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Proof step 77 from proof range-eq-splice-less (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ m < n → resize(ar, n)[m] = (# ar ≤ m ∧ m < n ⊃ zero;ar[m])

Rule argument

spec: <toplevel> name: resize-at seq: ⊦ m < n → resize(ar, n)[m] = (# ar ≤ m ∧ m < n ⊃ zero;ar[m]) subst: [m, n, ar] → [n1 + n3, (n1 + n4) + m1, ar0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n1 + n3, (n1 + n4) + m1, ar0