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Proof step 39 from proof range-extend (previous step)

n2 < m0 + m1, n0 + n2 < # ar0, (n1 + m0) + m1 ≤ # ar1, n + m1 ≤ # ar, n1 + m0 ≤ # ar1, n0 + m0 ≤ # ar0, n0 + m0 + m1 ≤ # ar0, ∀ n2. n2 < m1 → ar[n + n2] = ar1[(n1 + m0) + n2], ∀ n. n < m0 → ar0[n0 + n] = ar1[n1 + n] ⊦ (n2 < m0 ⊃ ar0[n0 + n2];ar[n2 + n - m0]) = ar1[n1 + n2]

User applied rule case distinction

And obtained the following new goals

Proof step 40:
n0 + n2 < # ar0, n2 < m0 + m1, n2 < m0, n0 + m0 + m1 ≤ # ar0, n0 + m0 ≤ # ar0, n1 + m0 ≤ # ar1, n + m1 ≤ # ar, (n1 + m0) + m1 ≤ # ar1, ∀ n. n < m0 → ar0[n0 + n] = ar1[n1 + n], ∀ n2. n2 < m1 → ar[n + n2] = ar1[(n1 + m0) + n2] ⊦ ar0[n0 + n2] = ar1[n1 + n2]
Proof step 42:
n0 + n2 < # ar0, n2 < m0 + m1, n0 + m0 + m1 ≤ # ar0, n0 + m0 ≤ # ar0, n1 + m0 ≤ # ar1, n + m1 ≤ # ar, (n1 + m0) + m1 ≤ # ar1, ∀ n. n < m0 → ar0[n0 + n] = ar1[n1 + n], ∀ n2. n2 < m1 → ar[n + n2] = ar1[(n1 + m0) + n2] ⊦ ar[n2 + n - m0] = ar1[n1 + n2], n2 < m0

Rule argument

pos: right 1

Proof step 39 from proof range-extend (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information