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Proof step 47 from proof copy-stream-append (previous step)

# buf1 = n2 + n1 + m, n0 + m ≤ # buf0 ⊦ ⌜n2⌝ + ⌜m⌝ = #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝
Proof step 49:
# buf1 = n2 + n1 + m, #(⌜buf0⌝ from n0) < ⌜m⌝ , n0 + m ≤ # buf0 ⊦ ⌜n2⌝ + ⌜m⌝ = #((⌜buf0⌝ from n0) to m) + #(⌜buf1⌝ from n1 + m)
Proof step 52:
# buf1 = n2 + n1 + m, n0 + m ≤ # buf0 ⊦ ⌜n2⌝ + ⌜m⌝ = ⌜m⌝ + #(⌜buf1⌝ from n1 + 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