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Proof step 9 from proof splice-resize-less (previous step)

n2 ≤ m0 ⊦ m0 = 0, resize(splice(ar0, n0, ar1, n1, m0), n2 + n1) = resize(splice(ar0, n0, ar1, n1, n2), n2 + n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 11:
n2 ≤ m0 ⊦ m0 = 0, # resize(splice(ar0, n0, ar1, n1, m0), n2 + n1) = # resize(splice(ar0, n0, ar1, n1, n2), n2 + n1) ∧ (∀ n. n < # resize(splice(ar0, n0, ar1, n1, m0), n2 + n1) → resize(splice(ar0, n0, ar1, n1, m0), n2 + n1)[n] = resize(splice(ar0, n0, ar1, n1, n2), n2 + n1)[n])

Rule argument

spec: array name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [resize(splice(ar0, n0, ar1, n1, n2), n2 + n1), resize(splice(ar0, n0, ar1, n1, m0), n2 + n1)] flags: <all paths>

Additional information

Used terms: resize(splice(ar0, n0, ar1, n1, n2), n2 + n1), resize(splice(ar0, n0, ar1, n1, m0), n2 + n1)