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Proof step 37 from proof truncate-same-iso (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[ino0] = mkfile(m2, md0, # links(ino0, dirs), content0), afs-cons(dirs, files0), m2 / VFS_PAGE_SIZE ∈ content0, ino0 ∈ files0 ⊦ m2 % VFS_PAGE_SIZE = 0, files0 ~ files0 [ino0, mkfile(m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ files0 ~ files1 ↔ (∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size))
Proof step 39:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[ino0] = mkfile(m2, md0, # links(ino0, dirs), content0), afs-cons(dirs, files0), ino0 ∈ files0, m2 / VFS_PAGE_SIZE ∈ content0 ⊦ m2 % VFS_PAGE_SIZE = 0, ∀ ino. ( ino ∈ files0 ↔ ino ∈ files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ ( ino ∈ files0 → files0[ino].size = files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [ino ] .size ∧ files0[ino].meta = files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [ino ] .meta ∧ files0[ino].nlink = files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [ino ] .nlink ∧ files0[ino].content.stream to files0[ino].size = files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [ino ] .content .stream to files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [ino ] .size)

Rule argument

spec: afs-stream name: files-iso seq: ⊦ files0 ~ files1 ↔ (∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size)) subst: [files1, files0] → [files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ], files0] flags: <all paths>

Additional information

Used terms: files0 [ino0, mkfile (m2, md0, # links(ino0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ], files0