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Proof step 38 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, 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)) = ((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 39:
⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n])
Proof step 40:
# 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, min(n3, n6, n1) ≤ n6 ⊦ n6 = 0, #(((content.stream from n0) to n) + ((content.stream from n0 + n) 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)) ∧ (∀ n2. ⌜n2⌝ < #(((content.stream from n0) to n) + ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1))) → (((content.stream from n0) to n) + ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)))[n2] = (((content.stream from n0) to min(n3, n6, n1) + n) + (⌜buf0⌝ from min(n3, n6, n1) + n))[n2])

Rule argument

spec: stream, inst: buffer-inf name: extensionality seq: ⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n]) subst: [σ2, σ] → [ ((content.stream from n0) to min(n3, n6, n1) + n) + (⌜buf0⌝ from min(n3, n6, n1) + n), ((content.stream from n0) to n) + ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1))] flags: <all paths>

Additional information

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