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Proof step 37 from proof refine-write-inode (previous step)

dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), m ≠ 0, fs0[ri[inodekey(m)]].inode?, 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), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ¬ adr1 ∈ fs0, asynced → boolvar1, ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∨ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m2 = fs0[ri[inodekey(m)]].size, fs0[ri[inodekey(m)]].directory ∧ m2 = fs0[ri[inodekey(m)]].size ∧ boolvar0 ∨ ¬ fs0[ri[inodekey(m)]].directory ∧ fs0[ri[inodekey(m)]].nsubdirs = 0 ∧ ¬ boolvar0 ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files (fs0[adr1, inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2)], ri[inodekey(m), adr1]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced → boolvar) ∧ ESUCCESS = err), ⟨if boolvar0 then dirs[m].meta := md else {files[m].meta := md; files[mkinode(m, md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2).ino].size := mkinode(m, md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2).size}; err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2)], ri[inodekey(m), adr1]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2)], ri[inodekey(m), adr1]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced → boolvar) ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
fs0[ri[inodekey(m)]] = inodenode(key, md0, boolvar2, m0, m1, m3), dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), fs0[ri[inodekey(m)]].inode?, fo.inodes?, orphans(fs0, ri).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(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, asynced → boolvar1, boolvar2 ∧ m2 = m3 ∧ boolvar0 ∨ ¬ boolvar2 ∧ m1 = 0 ∧ ¬ boolvar0, ¬ boolvar2 ∧ ¬ boolvar0 ∨ boolvar2 ∧ boolvar0 ∧ m2 = m3 ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) ∧ orphans(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced → boolvar) ∧ ESUCCESS = err), ⟨if boolvar0 then dirs[m].meta := md else {files[m].meta := md; files[mkinode(m, md, boolvar0, m0, m1, m2).ino].size := mkinode(m, md, boolvar0, m0, m1, m2).size}; err := ESUCCESS; 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(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced → boolvar) ∧ ESUCCESS = err), m = 0, adr1 ∈ fs0

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs0[ri[inodekey(m)]], key, md0, boolvar2, m0, m1, m3]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs0[ri[inodekey(m)]], key, md0, boolvar2, m0, m1, m3