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

files1[m] = mkfile(m1, md, m2, content), of1[fd] = mkfile(m, mode, m0), buf-opt = none, err = ESUCCESS, files = files1, inode = mkinode(m, md, false, m2, 0, m1), n1 ≠ 0, afs-cons(dirs, files1), of-cons(of1, dirs, files1), fd ∈ of1, n1 ≤ # buf ⊦ [afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced); 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}; file := of1[fd]] (err = 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 ∧ (err = EBADFD ∧ (fd ∈ of → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert program lemma

And obtained the following new goals

Proof step 36:
afs-cons(dirs, files0), files0 = files1, pageno = inode.size / VFS_PAGE_SIZE, buf-opt.none?, inode = getinode(ino, dirs, files0), inode.size = n, inode = inode0, ¬ inode.directory, ino ∈ files0 ⊦ [afs_truncate#(n, pageno; buf-opt, inode, bv, err, dirs, files1, asynced)] ( (err = ESUCCESS ⊃ files1[ino].content.stream from n = σ⊥ ∧ (∀ n0, n1, buf. n1 ≤ # buf → write-inv(n0, n0 + n1, inode, buf, 0, dirs, files1, files1)) ∧ files0 -- ino = files1 -- ino ;⌊err⌋ ) ∧ files0 ~ files1 ∧ inode = inode0)
Proof step 37:
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}; file := of1[fd]] (err = 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 ∧ (err = EBADFD ∧ (fd ∈ of → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err⌋ ) )), n1 = 0, inode.directory, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: <toplevel> name: truncate-inv seq: afs-cons(dirs, files0), files0 = files1, pageno = inode.size / VFS_PAGE_SIZE, buf-opt.none?, inode = getinode(ino, dirs, files0), inode.size = n, inode = inode0, ¬ inode.directory, ino ∈ files0 ⊦ [afs_truncate# (n, pageno; buf-opt, inode, bv, err, dirs, files1, asynced)] ( (err = ESUCCESS ⊃ files1[ino].content.stream from n = σ⊥ ∧ (∀ n0, n1, buf. n1 ≤ # buf → write-inv (n0, n0 + n1, inode, buf, 0, dirs, files1, files1)) ∧ files0 -- ino = files1 -- ino ;⌊err⌋ ) ∧ files0 ~ files1 ∧ inode = inode0) subst: [pageno, n, asynced, files1, dirs, err, bv, inode, buf-opt, ino, files0, inode0] → [m1 / VFS_PAGE_SIZE, m1, asynced, files, dirs, err, isdir, inode, buf-opt, m, files, inode] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ none.none?; (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)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)