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Proof step 20 from proof copy-stream-append (previous step)

# buf1 = n2 + n1 + m, ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m), n1 < # buf1, n3 < n2 + m, n1 + m ≤ # buf1, n0 + m ≤ # buf0 ⊦ (m ≤ n3 ⊃ buf1[n3 + n1];buf0[n3 + n0]) = (((⌜buf0⌝ from n0) to m) + (⌜buf1⌝ from n1 + m))[n3], ⌜n3⌝ < #((⌜buf0⌝ from n0) to m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# buf1 = n2 + n1 + m, ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m), n3 < n2 + m, n1 < # buf1, n0 + m ≤ # buf0, n1 + m ≤ # buf1 ⊦ (m ≤ n3 ⊃ buf1[n3 + n1];buf0[n3 + n0]) = (⌜buf1⌝ from n1 + m)[n3 - (#((⌜buf0⌝ from n0) to m)).n], ⌜n3⌝ < #((⌜buf0⌝ from n0) to m)

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)