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Proof step 45 from proof truncate-smaller (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ n ∈ content ∧ # content[n] = VFS_PAGE_SIZE → ⌜content[n]⌝ = (content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE
Proof step 47:
# content0[m1] = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + n1, files0[m] = mkfile(m0, md0, # links(m, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m ∈ files0, m1 ∈ content0 ⊦ [asynced := ?] ( (content0.stream to m1 * VFS_PAGE_SIZE) + (((content0.stream from m1 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE to n1) + (σ⊥ to n0)) + (content0.stream from VFS_PAGE_SIZE * m1 + VFS_PAGE_SIZE) to m1 * VFS_PAGE_SIZE + n1 = content0.stream to m1 * VFS_PAGE_SIZE + n1), n0 = 0, n1 = 0

Rule argument

spec: afs-stream name: at-content-stream seq: ⊦ n ∈ content ∧ # content[n] = VFS_PAGE_SIZE → ⌜content[n]⌝ = (content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE subst: [n, content] → [m1, content0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ #(content.stream from n) = ∞; (s)% ⊦ ⌜m⌝ < ∞; (s)% ⊦ # content.stream = ∞; (s) Used terms: m1, content0