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Proof step 254 from proof write-prepost (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files0 -- m = files -- m, files1 -- m = files -- m, files[m] = mkfile(m1, md, m3, content1), files0[m] = mkfile(m1, md, # links(m, dirs1), content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs1), content0), buf-opt = none, err2 = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, (content1.stream to m1).buf ≠ (content.stream to m1).buf, ino ≠ 0, n1 ≠ 0, m1 < m0, m1 < m0 + ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 255:
files0[ino] = mkfile(m0, md0, n2, content0), files1[ino] = mkfile(m1, md1, n3, content1), write-inv(n0, n1, mkinode(ino, md, false, m, m3, m2), buf, n, dirs, files0, files1) ⊦ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)
Proof step 256:
⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files -- m, files0 -- m = files -- m, files1[m] = mkfile(m1, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs1), content), files[m] = mkfile(m1, md, m3, content1), buf-opt = none, err2 = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, m1 < m0 + ino, m1 < m0, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, ino, dirs0, files0, files), files1 ~ files0, fd ∈ of1, m ∈ files, m ∈ files1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ((content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to m1).buf = (content.stream to m1).buf, ino = 0, n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: <toplevel> name: write-inv-stream seq: files0[ino] = mkfile(m0, md0, n2, content0), files1[ino] = mkfile(m1, md1, n3, content1), write-inv (n0, n1, mkinode(ino, md, false, m, m3, m2), buf, n, dirs, files0, files1) ⊦ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n) subst: [files0, ino, m0, md0, n2, content0, files1, m1, md1, n3, n0, n1, md, m, m3, m2, buf, n, dirs, content1] → [files0, m, m1, md, # links(m, dirs1), content, files, m1, md, m3, m0, m0 + n1, md, # links(m, dirs1), 0, m1, buf, ino, dirs0, content1] flags: <all paths>

Additional information

Used terms: files0, m, m1, md, # links(m, dirs1), content, files, m1, md, m3, m0, m0 + n1, md, # links(m, dirs1), 0, m1, buf, ino, dirs0, content1