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Proof step 60 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), n7 < n4 + min(n3, n6, n1), n7 < n6, n < # buf1, n5 < VFS_PAGE_SIZE, n7 < min(n3, n6, n1), 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 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)))[n7] = getbyte(n0 + n7 + n, content), n1 = 0, n3 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m]
Proof step 62:
# 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), n7 < min(n3, n6, n1), n5 < VFS_PAGE_SIZE, n < # buf1, n7 < n6, n7 < n4 + min(n3, n6, n1), ⌜n7⌝ < #((content.stream from n0 + n) to min(n3, n6, n1)), 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 + n) to min(n3, n6, n1))[n7] = getbyte(n0 + n7 + n, content), n1 = 0, n3 = 0

Rule argument

spec: stream, inst: buffer-inf name: get-append-ls seq: ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m] subst: [m, σ2, σ0] → [n7, ⌜buf0⌝ from n + min(n3, n6, n1), (content.stream from n0 + n) to min(n3, n6, n1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)% ⊦ #(content.stream from n) = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ .n = m; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n7, ⌜buf0⌝ from n + min(n3, n6, n1), (content.stream from n0 + n) to min(n3, n6, n1)