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Proof step 55 from proof read-inv-rec (previous step)

# buf0 = # buf1, # buf1 = n4 + n + min(n3, n6, n1), n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n5 < VFS_PAGE_SIZE, ⌜n2⌝ < ⌜n⌝ + ⌜min(n3, n6, n1)⌝ + #(⌜buf0⌝ from n + min(n3, n6, n1)), n2 < n + min(n3, n6, n1), n2 < # buf1, afs-cons(dirs, files), ino ∈ files, min(n3, n6, n1) ≤ n6, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, n + min(n3, n6, n1) ≤ # buf1, n3 + n ≤ # buf1, min(n3, n6, n1) + n ≤ # buf1 ⊦ (((content.stream from n0) to n) + ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)))[n2] = getbyte(n0 + n2, content), n6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m]
Proof step 57:
# buf1 = n4 + n + min(n3, n6, n1), # buf0 = # buf1, n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n2 < # buf1, n2 < n + min(n3, n6, n1), ⌜n2⌝ < ⌜n⌝ + ⌜min(n3, n6, n1)⌝ + #(⌜buf0⌝ from n + min(n3, n6, n1)), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, min(n3, n6, n1) + n ≤ # buf1, n3 + n ≤ # buf1, n + min(n3, n6, n1) ≤ # buf1, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, min(n3, n6, n1) ≤ n6 ⊦ (((content.stream from n0) to n) + ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)))[n2] = getbyte(n0 + n2, content), n6 = 0, ⌜n2⌝ < #((content.stream from n0) to n)
Proof step 65:
# buf1 = n4 + n + min(n3, n6, n1), # buf0 = # buf1, n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n2 < # buf1, n2 < n + min(n3, n6, n1), ⌜n2⌝ < ⌜n⌝ + ⌜min(n3, n6, n1)⌝ + #(⌜buf0⌝ from n + min(n3, n6, n1)), n5 < VFS_PAGE_SIZE, ⌜n2⌝ < #((content.stream from n0) to n), afs-cons(dirs, files), ino ∈ files, min(n3, n6, n1) + n ≤ # buf1, n3 + n ≤ # buf1, n + min(n3, n6, n1) ≤ # buf1, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, min(n3, n6, n1) ≤ n6 ⊦ ((content.stream from n0) to n)[n2] = getbyte(n0 + n2, content), n6 = 0

Rule argument

spec: stream, inst: buffer-inf name: get-append-ls seq: ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m] subst: [m, σ2, σ0] → [n2, ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)), (content.stream from n0) to n] flags: <all paths>

Additional information

Used terms: n2, ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)), (content.stream from n0) to n