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Proof step 66 from proof write-prepost (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, m3, content), buf-opt = none, err = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m1), n1 ≠ 0, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, ino, dirs0, files0, files), files1 ~ files0, m ∈ files, m ∈ files1, fd ∈ of1, n1 ≤ # buf, ino = 0 → files = files0, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ [if ino ≠ 0 then err0 := ESUCCESS; of := of1; n := n1; if err0 = ESUCCESS then let ino3 = m1 in {n := ino, ino1 := of1[fd].pos + ino; if ino ≠ 0 ∧ ino3 < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files; err0; asynced1); if err0 = ESUCCESS then afs_write_inode#(inode0; err0, dirs0, files; asynced1)}; ino2 := of1[fd].pos; if err0 ≠ ESUCCESS then n := (ino2 ≤ ino3 ⊃ ino3 - ino2;0), err0 := ESUCCESS; of[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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ ino ∈ files0 ∨ ino ∈ files1 → ( files0 ~ files1 ↔ files0 ~ files1 ∧ files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size)
Proof step 68:
⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files1[m].meta = files0[m].meta, files1[m].nlink = files0[m].nlink, files1[m].size = files0[m].size, files0[m] = mkfile(m2, md0, m3, content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), buf-opt = none, err = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m1), files1[m].content.stream to files1[m].size = files0[m].content.stream to files0[m].size, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files1, m ∈ files, n1 ≤ # buf, ino = 0 → files = files0, err0 = ESUCCESS ∨ ⌊err0⌋ , m ∈ files1 ∨ m ∈ files0 ⊦ [if ino ≠ 0 then err0 := ESUCCESS; of := of1; n := n1; if err0 = ESUCCESS then let ino3 = m1 in {n := ino, ino1 := of1[fd].pos + ino; if ino ≠ 0 ∧ ino3 < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files; err0; asynced1); if err0 = ESUCCESS then afs_write_inode#(inode0; err0, dirs0, files; asynced1)}; ino2 := of1[fd].pos; if err0 ≠ ESUCCESS then n := (ino2 ≤ ino3 ⊃ ino3 - ino2;0), err0 := ESUCCESS; of[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⌋ ) ), n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: afs-stream name: iso-unfold seq: ⊦ ino ∈ files0 ∨ ino ∈ files1 → ( files0 ~ files1 ↔ files0 ~ files1 ∧ files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size) subst: [ino, files1, files0] → [m, files0, files1] flags: <all paths>

Additional information

Used terms: m, files0, files1