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Proof step 51 from proof truncate-greater (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
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), m0 ∈ files0, m1 ∈ content0 ⊦ [asynced := ?] ( ( (content0.stream to m1 * VFS_PAGE_SIZE) + ((⌜content0[m1]⌝ 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))

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)