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Proof step 16 from proof read-inv-post (previous step)

# buf0 = # buf1, files[ino] = mkfile(m, md, # links(ino, dirs), content), buf1[n2] = (((content.stream from n0) to n) + (⌜buf0⌝ from n))[n2], ⌜# buf1⌝ = ⌜n⌝ + #(⌜buf0⌝ from n), n2 < # buf1, afs-cons(dirs, files), ino ∈ files, n0 + n ≤ n1, n0 + n ≤ m, n1 ≤ # buf1 + n0, n ≤ # buf1 ⊦ (n ≤ n2 ⊃ buf0[n2];getbyte(n2 + n0, content)) = buf1[n2]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m]
Proof step 18:
# buf0 = # buf1, buf1[n2] = (((content.stream from n0) to n) + (⌜buf0⌝ from n))[n2], files[ino] = mkfile(m, md, # links(ino, dirs), content), ⌜# buf1⌝ = ⌜n⌝ + #(⌜buf0⌝ from n), n2 < # buf1, afs-cons(dirs, files), ino ∈ files, n ≤ # buf1, n1 ≤ # buf1 + n0, n0 + n ≤ m, n0 + n ≤ n1 ⊦ (n ≤ n2 ⊃ buf0[n2];getbyte(n2 + n0, content)) = buf1[n2], ⌜n2⌝ < #((content.stream from n0) to n)
Proof step 23:
# buf0 = # buf1, buf1[n2] = ((content.stream from n0) to n)[n2], files[ino] = mkfile(m, md, # links(ino, dirs), content), ⌜# buf1⌝ = ⌜n⌝ + #(⌜buf0⌝ from n), n2 < # buf1, ⌜n2⌝ < #((content.stream from n0) to n), afs-cons(dirs, files), ino ∈ files, n ≤ # buf1, n1 ≤ # buf1 + n0, n0 + n ≤ m, n0 + n ≤ n1 ⊦ (n ≤ n2 ⊃ buf0[n2];getbyte(n2 + n0, content)) = buf1[n2]

Rule argument

spec: stream, inst: buffer-inf name: get-append-ls seq: ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m] subst: [m, σ2, σ0] → [n2, ⌜buf0⌝ from n, (content.stream from n0) to n] flags: <all paths>

Additional information

Used terms: n2, ⌜buf0⌝ from n, (content.stream from n0) to n