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Proof step 40 from proof writepage-afs-cons (previous step)

# buf2 = VFS_PAGE_SIZE, (ino1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, copy(buf0, ino0, buf2, ino, n)]) ;mkfile(m1, md0, # links(ino1, dirs), content0) ) = mkfile(m3, md1, m4, content1), dirs[ino1] = mkdir(m5, md2, m6, m7, entries), files[m] = mkfile(m0, md, # links(m, dirs), content), files[ino1] = mkfile(m1, md0, # links(ino1, dirs), content0), afs-cons(dirs, files), m ∈ files, ROOT_INO ∈ dirs, ino0 + n ≤ # buf0, ino + n ≤ VFS_PAGE_SIZE ⊦ ino1 ∈ dirs, (ino1 ∈ files → m4 = # links(ino1, dirs)) ∧ (ino1 ∈ files ∧ n0 ∈ content1 → # content1[n0] = VFS_PAGE_SIZE)

User applied rule case distinction

And obtained the following new goals

Proof step 41:
# buf2 = VFS_PAGE_SIZE, files[ino1] = mkfile(m1, md0, # links(ino1, dirs), content0), files[m] = mkfile(m0, md, # links(m, dirs), content), dirs[ino1] = mkdir(m5, md2, m6, m7, entries), ino1 = m, mkfile(m0, md, # links(m, dirs), content[pageno, copy(buf0, ino0, buf2, ino, n)]) = mkfile(m3, md1, m4, content1), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino + n ≤ VFS_PAGE_SIZE, ino0 + n ≤ # buf0 ⊦ ino1 ∈ dirs, (ino1 ∈ files → m4 = # links(ino1, dirs)) ∧ (ino1 ∈ files ∧ n0 ∈ content1 → # content1[n0] = VFS_PAGE_SIZE)

Rule argument

pos: left 2

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)