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Proof step 21 from proof copy-stream-append (previous step)

# 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝
Proof step 23:
# buf1 = n2 + n1 + m, ⌜# buf1⌝ = ⌜n1⌝ + #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m), #(⌜buf0⌝ from n0) < ⌜m⌝ , n1 < # buf1, n3 < n2 + m, n1 + m ≤ # buf1, n0 + m ≤ # buf0 ⊦ (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)
Proof step 26:
# buf1 = n2 + n1 + m, ⌜# buf1⌝ = ⌜n1⌝ + ⌜m⌝ + #(⌜buf1⌝ from n1 + m), n1 < # buf1, n3 < n2 + m, n1 + m ≤ # buf1, n0 + m ≤ # buf0 ⊦ (m ≤ n3 ⊃ buf1[n3 + n1];buf0[n3 + n0]) = (⌜buf1⌝ from n1 + m)[n3 - ⌜m⌝ .n], ⌜n3⌝ < ⌜m⌝ , #(⌜buf0⌝ from n0) < ⌜m⌝

Rule argument

spec: stream, inst: buffer-inf name: size-to seq: ¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ subst: [n, σ0] → [m, ⌜buf0⌝ from n0] flags: <all paths>

Additional information

Used terms: m, ⌜buf0⌝ from n0