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Proof step 66 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, orphans(fs1, ri).inodes?, fo.inodes?, afs-cons (abs-dirs(fs1, ri), abs-files(fs1, ri)[m, mkfile(fs1[ri[inodekey(m)]].size, fs1[ri[inodekey(m)]].meta, fs1[ri[inodekey(m)]].nlink, abs-content(m, fs1, ri)[pageno, buf])]), afs-cons(abs-dirs(fs1, ri), abs-files(fs1, ri)), file-node-cons(fs1, ri), log-cons(log0, fs1), orphans-cons(fs1, ri, orphans(fs1, ri)), replay-cons-strong(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs1, ri, orphans(fs1, ri), fi, fo, log0), inodekey(m) ∈ ri, asynced0 → boolvar0 ⊦ abs-files(fs1, ri) [m, mkfile(fs1[ri[inodekey(m)]].size, fs1[ri[inodekey(m)]].meta, fs1[ri[inodekey(m)]].nlink, abs-content(m, fs1, ri)[pageno, buf]) ] = abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
# buf = VFS_PAGE_SIZE, fo.inodes?, orphans(fs1, ri).inodes?, afs-cons(abs-dirs(fs1, ri), abs-files(fs1, ri)), afs-cons (abs-dirs(fs1, ri), abs-files(fs1, ri)[m, mkfile(fs1[ri[inodekey(m)]].size, fs1[ri[inodekey(m)]].meta, fs1[ri[inodekey(m)]].nlink, abs-content(m, fs1, ri)[pageno, buf])]), file-node-cons(fs1, ri), log-cons(log0, fs1), orphans-cons(fs1, ri, orphans(fs1, ri)), replay-cons-strong(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs1, ri, orphans(fs1, ri), fi, fo, log0), inodekey(m) ∈ ri, asynced0 → boolvar0 ⊦ fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1, ( inodekey(ino) ∈ ri ∧ ¬ fs1[ri[inodekey(ino)]].directory ↔ inodekey(ino) ∈ ri[datakey(m, pageno), adr1] ∧ ¬ (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).directory) ∧ ( inodekey(ino) ∈ ri ∧ ¬ fs1[ri[inodekey(ino)]].directory → (ino = m ⊃ mkfile(fs1[ri[inodekey(m)]].size, fs1[ri[inodekey(m)]].meta, fs1[ri[inodekey(m)]].nlink, abs-content(m, fs1, ri)[pageno, buf]) ;mkfile(fs1[ri[inodekey(ino)]].size, fs1[ri[inodekey(ino)]].meta, fs1[ri[inodekey(ino)]].nlink, abs-content(ino, fs1, ri)) ) = mkfile ((adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).size, (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).meta, (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).nlink, abs-content(ino, fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])))

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);%⊦ 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)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)%⊦ files = abs-files(fs, ri) ↔ (∀ ino. ( ino ∈ files ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory) ∧ (ino ∈ files → files[ino] = abs-file(ino, fs, ri))); (ss)