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Proof step 9 from proof fill-stream-append (previous step)

m + n = # buf, n0 < m + n ⊦ fill(buf, zero, n, m)[n0] = ((⌜buf⌝ to n) + (σ⊥ to m))[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m]
Proof step 11:
m + n = # buf, n0 < m + n ⊦ fill(buf, zero, n, m)[n0] = ((⌜buf⌝ to n) + (σ⊥ to m))[n0], ⌜n0⌝ < #(⌜buf⌝ to n)
Proof step 14:
m + n = # buf, n0 < m + n, ⌜n0⌝ < #(⌜buf⌝ to n) ⊦ fill(buf, zero, n, m)[n0] = (⌜buf⌝ to n)[n0]

Rule argument

spec: stream, inst: buffer-inf name: get-append-ls seq: ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m] subst: [m, σ2, σ0] → [n0, σ⊥ to m, ⌜buf⌝ to n] flags: <all paths>

Additional information

Used terms: n0, σ⊥ to m, ⌜buf⌝ to n