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Proof step 6 from proof refine-write (previous step)

dirs1 = dirs, err = err0, fs = abs-files(files), n = n0, ofh = abs-of(of), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), n0 ≤ # buf, psynced → asynced ⊦ [vfs_write#(fd, buf, user; n, err, of, dirs, files, asynced)] ( dirs1 = dirs → ⟨posix_write#(fd, buf, user, root; n0, err0, fs, ofh; psynced)⟩ (ofh = abs-of(of) ∧ fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ n = n0 ∧ err = err0))

User applied rule insert program lemma

And obtained the following new goals

Proof step 7:
afs-cons(dirs, files0), of-cons(of0, dirs, files0), files0 = files1, of0 = of1, n0 = n1, n0 ≤ # buf, file = of0[fd] ⊦ [vfs_write#(fd, buf, user; n1, err, of1, dirs, files1, asynced)] (err = ESUCCESS ⊃ (files1[file.ino].content.stream to files1[file.ino].size).buf = splice(buf, 0, (files0[file.ino].content.stream to files0[file.ino].size).buf, file.pos, n1) ∧ fd ∈ of0 ∧ of1 = of0[fd, file.pos:= (file.pos + n1)] ∧ n1 ≤ n0 ∧ file.ino ∈ files0 ∧ file.ino ∈ files1 ∧ files1[file.ino].meta = files0[file.ino].meta ∧ files1 -- file.ino = files0 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ;files1 ~ files0 ∧ of0 = of1 ∧ (err = EBADFD ∧ (fd ∈ of0 → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err⌋ ) )
Proof step 8:
of[fd] = of[fd], buf0 = buf, dirs1 = dirs, err = err0, fd0 = fd, file0 = of[fd], files = files, files2 = files, fs = abs-files(files), n = n0, n = n, n2 = n, of = of, of2 = of, ofh = abs-of(of), user0 = user, root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), n0 ≤ # buf, n ≤ # buf, psynced → asynced ⊦ [vfs_write#(fd, buf, user; n, err, of, dirs, files, asynced)] ( (err = ESUCCESS ⊃ (files[file0.ino].content.stream to files[file0.ino].size).buf = splice(buf0, 0, (files2[file0.ino].content.stream to files2[file0.ino].size).buf, file0.pos, n) ∧ fd0 ∈ of2 ∧ of = of2[fd0, file0.pos:= (file0.pos + n)] ∧ n ≤ n2 ∧ file0.ino ∈ files2 ∧ file0.ino ∈ files ∧ files[file0.ino].meta = files2[file0.ino].meta ∧ files -- file0.ino = files2 -- file0.ino ∧ (file0.mode = MODE_W ∨ file0.mode = MODE_RW) ;files ~ files2 ∧ of2 = of ∧ (err = EBADFD ∧ (fd0 ∈ of2 → file0.mode ≠ MODE_W ∧ file0.mode ≠ MODE_RW) ∨ ⌊err⌋ ) ) → dirs1 = dirs → ⟨posix_write#(fd, buf, user, root; n0, err0, fs, ofh; psynced)⟩ (ofh = abs-of(of) ∧ fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ n = n0 ∧ err = err0))

Rule argument

spec: vfs-contracts name: write-prepost-partial seq: afs-cons(dirs, files0), of-cons(of0, dirs, files0), files0 = files1, of0 = of1, n0 = n1, n0 ≤ # buf, file = of0[fd] ⊦ [vfs_write# (fd, buf, user; n1, err, of1, dirs, files1, asynced)] (err = ESUCCESS ⊃ ( files1[file.ino].content.stream to files1[file.ino].size ).buf = splice (buf, 0, ( files0[file.ino].content.stream to files0[file.ino].size ).buf, file.pos, n1) ∧ fd ∈ of0 ∧ of1 = of0[fd, file.pos:= (file.pos + n1)] ∧ n1 ≤ n0 ∧ file.ino ∈ files0 ∧ file.ino ∈ files1 ∧ files1[file.ino].meta = files0[file.ino].meta ∧ files1 -- file.ino = files0 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ; files1 ~ files0 ∧ of0 = of1 ∧ ( err = EBADFD ∧ (fd ∈ of0 → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err⌋ ) ) subst: [user, buf, fd, asynced, files1, dirs, of1, err, n1, file, files0, of0, n0] → [user, buf, fd, asynced, files, dirs, of, err, n, of[fd], files, of, n] flags: <all paths>

Proof step 6 from proof refine-write (previous step)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

Additional information