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Proof step 35 from proof write-prepost-partial (previous step)

inode.size = m1, m1 / VFS_PAGE_SIZE = inode.size / VFS_PAGE_SIZE, of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, m2, content), buf-opt = none, err = ESUCCESS, files = files1, files = files, files2 = files, ino3 = m, inode = mkinode(m, md, false, m2, 0, m1), inode = getinode(m, dirs, files), inode = inode, inode1 = inode, n0 = m1, pageno0 = m1 / VFS_PAGE_SIZE, buf-opt.none?, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of1, dirs, files1), fd ∈ of1, m ∈ files, n1 ≤ # buf ⊦ [afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced)] ( (err = ESUCCESS ⊃ files[ino3].content.stream from n0 = σ⊥ ∧ (∀ n0, n1, buf. n1 ≤ # buf → write-inv(n0, n0 + n1, inode, buf, 0, dirs, files, files)) ∧ files2 -- ino3 = files -- ino3 ;⌊err⌋ ) ∧ files2 ~ files ∧ inode = inode1 → [ino2 := of1[fd].pos; ino0 := 0; if err = ESUCCESS then vfs_write_loop#(ino2, inode, of1[fd].pos + n1, buf, dirs; ino0, err, files, asynced); if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = inode.size in {n := ino0, ino1 := ino2 + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}] (err = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content.stream to m1).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files1 ∧ m ∈ files ∧ files[m].meta = md ∧ 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⌋ ) )), n1 = 0, inode.directory, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
files1[m].nlink = # links(m, dirs), files1[m] = mkfile(files1[m].size, files1[m].meta, # links(m, dirs), content), of1[fd] = mkfile(m, mode, m0), buf-opt = none, err = ESUCCESS, files = files1, inode = mkinode(m, files1[m].meta, false, # links(m, dirs), 0, files1[m].size), n1 ≠ 0, afs-cons(dirs, files1), of-cons(of1, dirs, files1), fd ∈ of1, m ∈ files1, n1 ≤ # buf ⊦ [afs_truncate#(files1[m].size, files1[m].size / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced)] ( (err = ESUCCESS ⊃ files[m].content.stream from files1[m].size = σ⊥ ∧ (∀ n0, n1, buf. n1 ≤ # buf → write-inv(n0, n0 + n1, mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size), buf, 0, dirs, files, files)) ∧ files1 -- m = files -- m ;⌊err⌋ ) ∧ files1 ~ files ∧ inode = mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) → [ino2 := of1[fd].pos; ino0 := 0; if err = ESUCCESS then vfs_write_loop#(ino2, inode, of1[fd].pos + n1, buf, dirs; ino0, err, files, asynced); if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = inode.size in {n := ino0, ino1 := ino2 + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}] (err = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content.stream to files1[m].size).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files ∧ files[m].meta = files1[m].meta ∧ 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⌋ ) )), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ none.none?; (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)