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Proof step 45 from proof truncate-same-iso (previous step)

VFS_PAGE_SIZE = n0 + m % VFS_PAGE_SIZE, files0[ino0] = mkfile(m, md, # links(ino0, dirs), content), afs-cons(dirs, files0), m / VFS_PAGE_SIZE ∈ content, ino0 ∈ files0 ⊦ m % VFS_PAGE_SIZE = 0, content.stream to m = content[m / VFS_PAGE_SIZE, fill(content[m / VFS_PAGE_SIZE], zero, m % VFS_PAGE_SIZE, n0)].stream to m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ # buf = VFS_PAGE_SIZE → content[n, buf].stream = (content.stream to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (content.stream from (n + 1) * VFS_PAGE_SIZE)
Proof step 47:
# fill(content[m / VFS_PAGE_SIZE], zero, m % VFS_PAGE_SIZE, n0) = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m % VFS_PAGE_SIZE, files0[ino0] = mkfile(m, md, # links(ino0, dirs), content), afs-cons(dirs, files0), ino0 ∈ files0, m / VFS_PAGE_SIZE ∈ content ⊦ m % VFS_PAGE_SIZE = 0, content.stream to m = (content.stream to m / VFS_PAGE_SIZE * VFS_PAGE_SIZE) + ⌜fill(content[m / VFS_PAGE_SIZE], zero, m % VFS_PAGE_SIZE, n0)⌝ + (content.stream from (m / VFS_PAGE_SIZE + 1) * VFS_PAGE_SIZE) to m

Rule argument

spec: afs-stream name: content-write seq: ⊦ # buf = VFS_PAGE_SIZE → content[n, buf].stream = (content.stream to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (content.stream from (n + 1) * VFS_PAGE_SIZE) subst: [buf, n, content] → [fill (content[m / VFS_PAGE_SIZE], zero, m % VFS_PAGE_SIZE, n0), m / VFS_PAGE_SIZE, content] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # fill(buf, d, m, n) = # buf; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s) Used terms: fill(content[m / VFS_PAGE_SIZE], zero, m % VFS_PAGE_SIZE, n0), m / VFS_PAGE_SIZE, content