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Proof step 93 from proof write-prepost (previous step)

⟨afs_truncate#(m2, m2 / VFS_PAGE_SIZE; buf-opt, inode1, isdir, err0, dirs1, files1, asynced)⟩ ( buf-opt = buf-opt0 ∧ inode1 = mkinode(m, md0, false, m3, 0, m2) ∧ (isdir ↔ isdir0) ∧ err0 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), # links(m, dirs1) = m3, files1 -- m = files0 -- m, files0[m] = mkfile(m2, md0, m3, content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m2, md0, m3, content0), files[m] = mkfile(m1, md, m3, content1), buf-opt = none, err0 = ESUCCESS, content.stream from m2 = σ⊥, inode1 = mkinode(m, md0, false, m3, 0, m2), content0.stream to m2 = content.stream to m2, m2 < m0 + ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md0, false, m3, 0, m2), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md0, false, m3, 0, m2), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ [ {if mkinode(m, md0, false, m3, 0, of1[fd].pos + ino).directory then dirs0[mkinode(m, md0, false, m3, 0, of1[fd].pos + ino).ino].meta := mkinode(m, md0, false, m3, 0, of1[fd].pos + ino).meta else {files[mkinode(m, md0, false, # links(m, dirs1), 0, of1[fd].pos + ino).ino].meta := mkinode(m, md0, false, # links(m, dirs1), 0, of1[fd].pos + ino).meta; files[mkinode(m, md0, false, # links(m, dirs1), 0, of1[fd].pos + ino).ino].size := mkinode(m, md0, false, # links(m, dirs1), 0, of1[fd].pos + ino).size}; err := ESUCCESS} or fail#(; ; err); asynced := ?; ino2 := of1[fd].pos; n := ino; err0 := err; if err0 ≠ ESUCCESS then n := (ino2 ≤ m2 ⊃ m2 - 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 94:
⊦ files0[ino] = mkfile(m0, md0, n2, content0) ∧ files1[ino] = mkfile(m1, md1, n3, content1) ∧ write-inv(n0, n1, mkinode(ino, md, false, m, n4, m2), buf, n, dirs, files0, files1) → m0 = m1 ∧ md0 = md1
Proof step 95:
⟨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, ino ≠ 0, n1 ≠ 0, 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⌋ ⊦ [ {if mkinode(m, md, false, # links(m, dirs1), 0, of1[fd].pos + ino).directory then dirs0[mkinode(m, md, false, # links(m, dirs1), 0, of1[fd].pos + ino).ino].meta := mkinode(m, md, false, # links(m, dirs1), 0, of1[fd].pos + ino).meta else {files[mkinode(m, md, false, # links(m, dirs1), 0, of1[fd].pos + ino).ino].meta := mkinode(m, md, false, # links(m, dirs1), 0, of1[fd].pos + ino).meta; files[mkinode(m, md, false, # links(m, dirs1), 0, of1[fd].pos + ino).ino].size := mkinode(m, md, false, # links(m, dirs1), 0, of1[fd].pos + ino).size}; err := ESUCCESS} or 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⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: write-inv-meta: ⊦ files0[ino] = mkfile(m0, md0, n2, content0) ∧ files1[ino] = mkfile(m1, md1, n3, content1) ∧ write-inv (n0, n1, mkinode(ino, md, false, m, n4, m2), buf, n, dirs, files0, files1) → m0 = m1 ∧ md0 = md1;