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Proof step 55 from proof truncate-greater (previous step)

VFS_PAGE_SIZE = n0 + n2, files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n2 ≠ 0, n2 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m1 ∈ content0, m0 ∈ files0 ⊦ [asynced := ?] ( ( (content0.stream to m1 * VFS_PAGE_SIZE) + ((content0.stream from m1 * VFS_PAGE_SIZE) to n2) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE) + σ⊥ to n1 + m1 * VFS_PAGE_SIZE + n2 = (content0.stream to m1 * VFS_PAGE_SIZE + n2) + (σ⊥ to n1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4
Proof step 57:
VFS_PAGE_SIZE = n0 + n2, files0[m0] = mkfile(m, md0, # links(m0, dirs), content0), n2 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m0 ∈ files0, m1 ∈ content0 ⊦ [asynced := ?] ( ( ((content0.stream to m1 * VFS_PAGE_SIZE) + ((content0.stream from m1 * VFS_PAGE_SIZE) to n2)) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE) + σ⊥ to n1 + m1 * VFS_PAGE_SIZE + n2 = (content0.stream to m1 * VFS_PAGE_SIZE + n2) + (σ⊥ to n1)), n0 = 0, n1 = 0, n2 = 0

Rule argument

spec: stream, inst: buffer-inf name: append-assoc seq: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4 subst: [σ4, σ3, σ0] → [content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE, σ⊥ to n0, (content0.stream to m1 * VFS_PAGE_SIZE) + ((content0.stream from m1 * VFS_PAGE_SIZE) to n2)] flags: <all paths>

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf] Used terms: content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE, σ⊥ to n0, (content0.stream to m1 * VFS_PAGE_SIZE) + ((content0.stream from m1 * VFS_PAGE_SIZE) to n2)