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Proof step 53 from proof truncate-empty (previous step)

VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ content0, ino0 ∈ files1 ⊦ [asynced := ?] ( ( (content0.stream to m0 * VFS_PAGE_SIZE) + ((content0.stream from m0 * VFS_PAGE_SIZE) to n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE + n1 = σ⊥)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4
Proof step 55:
VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino0 ∈ files1, m0 ∈ content0 ⊦ [asynced := ?] ( ( ((content0.stream to m0 * VFS_PAGE_SIZE) + ((content0.stream from m0 * VFS_PAGE_SIZE) to n1)) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE + n1 = σ⊥), n0 = 0, n1 = 0

Rule argument

spec: stream, inst: buffer-inf name: append-assoc seq: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4 subst: [σ4, σ3, σ0] → [ (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE), (content0.stream from m0 * VFS_PAGE_SIZE) to n1, content0.stream to m0 * VFS_PAGE_SIZE] flags: <rotated> <all paths>

Additional information

Used terms: (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE), (content0.stream from m0 * VFS_PAGE_SIZE) to n1, content0.stream to m0 * VFS_PAGE_SIZE