Proof step 75 from proof write-prepost-partial (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

• Proof step 76:

  ⟨afs_truncate#(m2, m2 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files1[m] = mkfile(m2, md0, # links(m, dirs), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, # links(m, dirs), content), buf-opt = none, err = ESUCCESS, content.stream from m2 = σ⊥, inode = mkinode(m, md0, false, # links(m, dirs), 0, m2), inode0 = mkinode(m, md0, false, # links(m, dirs), 0, m2), content0.stream to m2 = content.stream to m2, m2 < of1[fd].pos + ino, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs), 0, m2), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs), 0, m2), buf, ino, dirs0, files0, files), files1 ~ files0, fd ∈ of1, m ∈ files, m ∈ files1, n1 ≤ # buf, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ [inode0 := mkinode(m, md0, false, # links(m, dirs), 0, of1[fd].pos + ino); afs_check_commit#(dirs0, files; err; asynced1); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs0, files; asynced1); ino2 := of1[fd].pos; n := ino; if err ≠ ESUCCESS then n := (ino2 ≤ m2 ⊃ m2 - ino2;0), err := ESUCCESS; of := of1[fd, of1[fd].pos:= (ino2 + n)]] (err = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content0.stream to m2).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files ∧ files[m].meta = md0 ∧ files -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err = EBADFD ∧ (fd ∈ of → of[fd].mode ≠ MODE_W ∧ of[fd].mode ≠ MODE_RW) ∨ ⌊err⌋ ) ), ino = 0, n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

• Proof step 259:

  ⟨afs_truncate#(m2, m2 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files1[m] = mkfile(m2, md0, # links(m, dirs), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, # links(m, dirs), content), buf-opt = none, err = ESUCCESS, content.stream from m2 = σ⊥, inode = mkinode(m, md0, false, # links(m, dirs), 0, m2), inode0 = mkinode(m, md0, false, # links(m, dirs), 0, m2), content0.stream to m2 = content.stream to m2, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs), 0, m2), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs), 0, m2), buf, ino, dirs0, files0, files), files1 ~ files0, fd ∈ of1, m ∈ files, m ∈ files1, n1 ≤ # buf, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ [skip; ino2 := of1[fd].pos; n := ino; if err ≠ ESUCCESS then n := (ino2 ≤ m2 ⊃ m2 - ino2;0), err := ESUCCESS; of := of1[fd, of1[fd].pos:= (ino2 + n)]] (err = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content0.stream to m2).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files ∧ files[m].meta = md0 ∧ files -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err = EBADFD ∧ (fd ∈ of → of[fd].mode ≠ MODE_W ∧ of[fd].mode ≠ MODE_RW) ∨ ⌊err⌋ ) ), ino = 0, n1 = 0, m2 < of1[fd].pos + ino, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

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