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Proof step 72 from proof range-eq-splice-less (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 73:
ar2[n2 + n3] = (n3 < n4 ⊃ resize(ar0, (n1 + n4) + m1)[n1 + n3];ar[n3 + n - n4]), n3 < n4 + m0, n3 < m0, n3 < m1, # ar0 < (n1 + n4) + m1, # ar0 < (n1 + n4) + m0, n3 < n4 + m1, n3 < n4, n2 + m1 ≤ # ar2, n + m0 ≤ # ar, m1 ≤ m0 ⊦ ar2[n2 + n3] = resize(ar0, (n1 + n4) + m0)[n1 + n3]

Rule argument

pos: right 1

Proof step 72 from proof range-eq-splice-less (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information