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Proof step 38 from proof write-prepost (previous step)

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}; 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 39:
of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content), files1[m] = mkfile(m1, md, m2, content0), buf-opt = none, err = ESUCCESS, files = files1, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), m2 = # links(m, dirs), afs-cons(dirs, files1), of-cons(of1, dirs, files1), m ∈ files1, fd ∈ of1, n1 ≤ # buf ⊦ [afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced)] ( (err = ESUCCESS ⊃ files[m].content.stream from m1 = σ⊥ ∧ (∀ n0, n1, buf. n1 ≤ # buf → write-inv(n0, n0 + n1, mkinode(m, md, false, m2, 0, m1), buf, 0, dirs, files, files)) ∧ files1 -- m = files -- m ;⌊err⌋ ) ∧ files1 ~ files ∧ inode = mkinode(m, md, false, m2, 0, m1) → [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, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files1[m], m1, md, m2, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files1[m], m1, md, m2, content0