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Proof step 115 from proof write-prepost (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode1, isdir, err0, dirs1, files1, asynced)⟩ ( buf-opt = buf-opt0 ∧ inode1 = mkinode(m, md, false, m3, 0, m1) ∧ (isdir ↔ isdir0) ∧ err0 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), # links(m, dirs1) = m3, files1 -- m = files0 -- m, files[m] = mkfile(m1, md, # links(m, dirs1), content1), files1[m] = mkfile(m1, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs1), content), buf-opt = none, err0 = ESUCCESS, content.stream from m1 = σ⊥, inode1 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, 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, 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, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ [fail#(; ; err); asynced := ?; ino2 := of1[fd].pos; n := ino; err0 := err; if err0 ≠ ESUCCESS then n := (ino2 ≤ m1 ⊃ m1 - ino2;0), err0 := ESUCCESS; of := of1[fd, of1[fd].pos:= (ino2 + n)]; file := of1[fd]] (err0 = ESUCCESS ⊃ (files[file.ino].content.stream to files[file.ino].size).buf = splice(buf, 0, (files1[file.ino].content.stream to files1[file.ino].size).buf, file.pos, n) ∧ of = of1[fd, file.pos:= (file.pos + n)] ∧ n ≤ n1 ∧ file.ino ∈ files1 ∧ file.ino ∈ files ∧ files[file.ino].meta = files1[file.ino].meta ∧ files -- file.ino = files1 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err0 = EBADFD ∧ (fd ∈ of → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err0⌋ ) ), ino = 0, n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 116:
⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode1, isdir, err0, dirs1, files1, asynced)⟩ ( buf-opt = buf-opt0 ∧ inode1 = mkinode(m, md, false, m3, 0, m1) ∧ (isdir ↔ isdir0) ∧ err0 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), # links(m, dirs1) = m3, files1 -- m = files0 -- m, files0[m] = mkfile(m1, md, # links(m, dirs1), content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs1), content0), files[m] = mkfile(m1, md, # links(m, dirs1), content1), buf-opt = none, err0 = ESUCCESS, content.stream from m1 = σ⊥, inode1 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, 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, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ [choose err0 with ⌊err0⌋ in err := err0; asynced := ?; ino2 := of1[fd].pos; n := ino; err0 := err; if err0 ≠ ESUCCESS then n := (ino2 ≤ m1 ⊃ m1 - ino2;0), err0 := ESUCCESS; of := of1[fd, of1[fd].pos:= (ino2 + n)]; file := of1[fd]] (err0 = ESUCCESS ⊃ (files[file.ino].content.stream to files[file.ino].size).buf = splice(buf, 0, (files1[file.ino].content.stream to files1[file.ino].size).buf, file.pos, n) ∧ of = of1[fd, file.pos:= (file.pos + n)] ∧ n ≤ n1 ∧ file.ino ∈ files1 ∧ file.ino ∈ files ∧ files[file.ino].meta = files1[file.ino].meta ∧ files -- file.ino = files1 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err0 = EBADFD ∧ (fd ∈ of → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err0⌋ ) ), ino = 0, n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};