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Proof step 81 from proof write-inv-rec (previous step)

n0 + n = m0 * VFS_PAGE_SIZE + n2, ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + (((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) + ((⌜buf⌝ from n) to m) = (content.stream to n0) + (⌜buf⌝ to n + m), files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), files0[ino] = mkfile(m2, md0, m4, content), afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, m0 * VFS_PAGE_SIZE ≤ n1, n + m ≤ # buf, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m0 * VFS_PAGE_SIZE ≤ # buf + n0 ⊦ ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + (((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) + ((⌜buf⌝ from n) to m) + ((content.stream from (n0 + n) + m) to n4) + (content.stream from (n0 + n) + n4 + m) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m), n4 + m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 82:
⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4
Proof step 83:
((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + (((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) + ((⌜buf⌝ from n) to m) = (content.stream to n0) + (⌜buf⌝ to n + m), n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * VFS_PAGE_SIZE ≤ # buf + n0, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * VFS_PAGE_SIZE ≤ n1 ⊦ n4 + m = 0, ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + (((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) + ((⌜buf⌝ from n) to m) + ((content.stream from (n0 + n) + m) to n4) + (content.stream from (n0 + n) + n4 + m) = ((content.stream to n0) + (⌜buf⌝ to n + m)) + (content.stream from n0 + n + m)

Rule argument

spec: stream, inst: buffer-inf name: append-assoc seq: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4 subst: [σ4, σ3, σ0] → [content.stream from n0 + n + m, ⌜buf⌝ to n + m, content.stream to n0] flags: <rotated> <all paths>

Additional information

Used terms: content.stream from n0 + n + m, ⌜buf⌝ to n + m, content.stream to n0