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Proof step 8 from proof copy-stream-append (previous step)

# buf1 = n2 + n1 + m, n1 + m ≤ # buf1, n0 + m ≤ # buf0 ⊦ ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m) ∧ (n < # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ [n] = ((⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + (⌜buf1⌝ from n1 + m))[n])

User applied rule cut formula

And obtained the following new goals

Proof step 9:
# buf1 = n2 + n1 + m, ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m), n0 + m ≤ # buf0, n1 + m ≤ # buf1 ⊦ ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m) ∧ (n < # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ [n] = ((⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + (⌜buf1⌝ from n1 + m))[n])
Proof step 42:
# buf1 = n2 + n1 + m, n0 + m ≤ # buf0, n1 + m ≤ # buf1 ⊦ ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m), ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m) ∧ (n < # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ [n] = ((⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + (⌜buf1⌝ from n1 + m))[n])

Rule argument

fma: ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m)

Additional information

Used formulas: ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m)