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Proof step 24 from proof refine-write-inode (previous step)

dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), m ≠ 0, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), ¬ adr1 ∈ fs0, fs0[(∅)[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO → inodekey(m) ∈ ri, asynced → boolvar1, inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∨ inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri[inodekey(m)]].size, inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m2 = fs0[ri[inodekey(m)]].size ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar0 ⊦ ⟨afs_write_inode#(mkinode(m, md, boolvar0, m0, m1, m2); err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) ∧ files = abs-files(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) ∧ orphans (abs-dirs(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]), abs-files(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1])) = abs-keys(orphans(fs0, ri)) ∧ (asynced → boolvar) ∧ ESUCCESS = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 25:
afs-cons(dirs, files), pre-write-inode(inode, dirs, files) ⊦ ⟪afs_write_inode#(inode; err, dirs, files; asynced)⟫ afs-cons(dirs, files)
Proof step 26:
dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), inode0 = mkinode(m, md, boolvar0, m0, m1, m2), fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), afs-cons(dirs, files), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), pre-write-inode(mkinode(m, md, boolvar0, m0, m1, m2), dirs, files), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), asynced → boolvar1, fs0[(∅)[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO → inodekey(m) ∈ ri, inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m2 = fs0[ri[inodekey(m)]].size ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar0, inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∨ inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri[inodekey(m)]].size ⊦ ⟨afs_write_inode#(mkinode(m, md, boolvar0, m0, m1, m2); err0, dirs, files; asynced)⟩ ( afs-cons(dirs, files) → dirs = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) ∧ files = abs-files(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) ∧ orphans (abs-dirs(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]), abs-files(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1])) = abs-keys(orphans(fs0, ri)) ∧ (asynced → boolvar) ∧ ESUCCESS = err0), m = 0, adr1 ∈ fs0

Rule argument

spec: afs-asm name: inv-write_inode seq: afs-cons(dirs, files), pre-write-inode(inode, dirs, files) ⊦ ⟪afs_write_inode#(inode; err, dirs, files; asynced)⟫ afs-cons(dirs, files) subst: [inode, files, dirs, err, asynced] → [mkinode(m, md, boolvar0, m0, m1, m2), files, dirs, err0, asynced] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)