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Proof step 29 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, afs-cons(dirs, files), ino ∈ files, 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) + (⌜buf0⌝ from n) to n) + ((content.stream from m0 * VFS_PAGE_SIZE from n5) to n6 to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)) = ((content.stream from n0) to min(n3, n6, n1) + n) + (⌜buf0⌝ from min(n3, n6, n1) + n), n6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ ¬ # σ0 < ⌜m + n⌝ → σ0 from m from n = σ0 from m + n
Proof step 31:
# 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), 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 ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((content.stream from m0 * VFS_PAGE_SIZE + n5) to n6 to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)) = ((content.stream from n0) to min(n3, n6, n1) + n) + (⌜buf0⌝ from min(n3, n6, n1) + n), n6 = 0, # content.stream < ⌜m0 * VFS_PAGE_SIZE + n5⌝

Rule argument

spec: stream, inst: buffer-inf name: from-from seq: ⊦ ¬ # σ0 < ⌜m + n⌝ → σ0 from m from n = σ0 from m + n subst: [n, m, σ0] → [n5, m0 * VFS_PAGE_SIZE, content.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ ∞ < n∞; (s) Used terms: n5, m0 * VFS_PAGE_SIZE, content.stream