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Proof step 50 from proof write-prepost-partial (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⊥, ino0 = 0, 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), files1 ~ files0, m ∈ files1, fd ∈ of1, n1 ≤ # buf ⊦ [vfs_write_loop#(of1[fd].pos, mkinode(m, md, false, # links(m, dirs), 0, m1), of1[fd].pos + n1, buf, dirs0; ino0, err, files0, asynced0); if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = m1 in {n := ino0, ino1 := of1[fd].pos + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files0; err; asynced0); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs0, files0; asynced0)}; ino2 := of1[fd].pos; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}] (err = ESUCCESS ⊃ (files0[m].content.stream to files0[m].size).buf = splice(buf, 0, (content0.stream to m1).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files0 ∧ files0[m].meta = md ∧ files0 -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files0 ~ files1 ∧ of1 = of ∧ (err = EBADFD ∧ (fd ∈ of → of[fd].mode ≠ MODE_W ∧ of[fd].mode ≠ MODE_RW) ∨ ⌊err⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert program lemma

And obtained the following new goals

Proof step 51:
write-inv(n0, n1, inode, buf, n, dirs, files0, files1) ⊦ [vfs_write_loop#(n0, inode, n1, buf, dirs; n, err, files1, asynced)] write-inv(n0, n1, inode, buf, n, dirs, files0, files1)
Proof step 52:
⟨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, 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, buf0 = buf, dirs1 = dirs0, err = ESUCCESS, files = files0, content.stream from m1 = σ⊥, ino0 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m1), inode1 = mkinode(m, md, false, # links(m, dirs), 0, m1), n2 = of1[fd].pos, n3 = of1[fd].pos + n1, 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(of1[fd].pos, of1[fd].pos + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, ino0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files1, n1 ≤ # buf ⊦ [vfs_write_loop#(of1[fd].pos, mkinode(m, md, false, # links(m, dirs), 0, m1), of1[fd].pos + n1, buf, dirs0; ino0, err, files0, asynced0)] ( write-inv(n2, n3, inode1, buf0, ino0, dirs1, files, files0) → [if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = m1 in {n := ino0, ino1 := of1[fd].pos + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files0; err; asynced0); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs0, files0; asynced0)}; ino2 := of1[fd].pos; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}] (err = ESUCCESS ⊃ (files0[m].content.stream to files0[m].size).buf = splice(buf, 0, (content0.stream to m1).buf, m0, n) ∧ of = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files0 ∧ files0[m].meta = md ∧ files0 -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ;files0 ~ files1 ∧ of1 = of ∧ (err = EBADFD ∧ (fd ∈ of → of[fd].mode ≠ MODE_W ∧ of[fd].mode ≠ MODE_RW) ∨ ⌊err⌋ ) )), n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: <toplevel> name: write-loop-inv seq: write-inv(n0, n1, inode, buf, n, dirs, files0, files1) ⊦ [vfs_write_loop# (n0, inode, n1, buf, dirs; n, err, files1, asynced)] write-inv(n0, n1, inode, buf, n, dirs, files0, files1) subst: [dirs, buf, n1, inode, n0, asynced, files1, err, n, files0] → [dirs0, buf, of1[fd].pos + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), of1[fd].pos, asynced0, files0, err, ino0, files0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkfile(m, mode, m0).pos = m0; (s)