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Proof step 17 from proof truncate-inv (previous step)

⟨afs_truncate#(m, m / VFS_PAGE_SIZE; buf-opt, inode, bv, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (bv ↔ bv0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files ∧ (asynced ↔ asynced0)), files1[ino] = mkfile(m, md0, # links(ino, dirs), content), buf-opt = none, inode = mkinode(ino, md0, false, # links(ino, dirs), 0, m), afs-cons(dirs, files1), afs-cons(dirs0, files), files1 ~ files, ino ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files[ino].content.stream from m = σ⊥ ∧ (n0 ≤ # buf → write-inv(n, n + n0, mkinode(ino, md0, false, # links(ino, dirs), 0, m), buf, 0, dirs0, files, files)) ∧ files1 -- ino = files -- ino ;⌊err0⌋ ) ∧ inode0 = mkinode(ino, md0, false, # links(ino, dirs), 0, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ write-inv(n0, n1, inode, buf, n, dirs, files0, files1) ↔ afs-cons(dirs, files1) ∧ inode.ino ∈ files0 ∧ inode.ino ∈ files1 ∧ files0[inode.ino].size = inode.size ∧ files1[inode.ino].size = files0[inode.ino].size ∧ files1[inode.ino].meta = files0[inode.ino].meta ∧ files1 -- inode.ino = files0 -- inode.ino ∧ n0 + n ≤ n1 ∧ n1 - n0 ≤ # buf ∧ write-inv(n0, n1, buf, n, files0[inode.ino].content, files1[inode.ino].content)
Proof step 19:
⟨afs_truncate#(m, m / VFS_PAGE_SIZE; buf-opt, inode, bv, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (bv ↔ bv0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files ∧ (asynced ↔ asynced0)), files1[ino] = mkfile(m, md0, # links(ino, dirs), content), buf-opt = none, inode = mkinode(ino, md0, false, # links(ino, dirs), 0, m), afs-cons(dirs0, files), afs-cons(dirs, files1), files1 ~ files, ino ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files[ino].content.stream from m = σ⊥ ∧ ( n0 ≤ # buf → afs-cons(dirs0, files) ∧ mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino ∈ files ∧ mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino ∈ files ∧ files[mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino].size = mkinode(ino, md0, false, # links(ino, dirs), 0, m).size ∧ files[mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino].size = files[mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino].size ∧ files[mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino].meta = files[mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino].meta ∧ files -- mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino = files -- mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino ∧ n + 0 ≤ n + n0 ∧ n + n0 - n ≤ # buf ∧ write-inv (n, n + n0, buf, 0, files[mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino].content, files[mkinode(ino, md0, false, # links(ino, dirs), 0, m).ino].content)) ∧ files1 -- ino = files -- ino ;⌊err0⌋ ) ∧ inode0 = mkinode(ino, md0, false, # links(ino, dirs), 0, m)

Rule argument

spec: <toplevel> name: write-inv-strong seq: ⊦ write-inv(n0, n1, inode, buf, n, dirs, files0, files1) ↔ afs-cons(dirs, files1) ∧ inode.ino ∈ files0 ∧ inode.ino ∈ files1 ∧ files0[inode.ino].size = inode.size ∧ files1[inode.ino].size = files0[inode.ino].size ∧ files1[inode.ino].meta = files0[inode.ino].meta ∧ files1 -- inode.ino = files0 -- inode.ino ∧ n0 + n ≤ n1 ∧ n1 - n0 ≤ # buf ∧ write-inv (n0, n1, buf, n, files0[inode.ino].content, files1[inode.ino].content) subst: [files1, files0, dirs, n, buf, inode, n1, n0] → [files, files, dirs0, 0, buf, mkinode(ino, md0, false, # links(ino, dirs), 0, m), n + n0, n] flags: <all paths>

Additional information

Used terms: files, files, dirs0, 0, buf, mkinode(ino, md0, false, # links(ino, dirs), 0, m), n + n0, n