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Proof step 76 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, inodekey(ino) ∈ ri, asynced0 → boolvar0 ⊦ adr1 = ri[inodekey(ino)], fs1[ri[inodekey(m)]].directory, fs1[ri[inodekey(ino)]].directory, adr1 ∈ fs1, (¬ fs1[ri[inodekey(ino)]].directory → inodekey(ino) ∈ ri[datakey(m, pageno), adr1]) ∧ ( ¬ 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 (fs1[ri[inodekey(ino)]].size, fs1[ri[inodekey(ino)]].meta, fs1[ri[inodekey(ino)]].nlink, abs-content(ino, fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
# 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, inodekey(ino) ∈ ri, asynced0 → boolvar0 ⊦ (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 (fs1[ri[inodekey(ino)]].size, fs1[ri[inodekey(ino)]].meta, fs1[ri[inodekey(ino)]].nlink, abs-content(ino, fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])), adr1 = ri[inodekey(ino)], fs1[ri[inodekey(m)]].directory, fs1[ri[inodekey(ino)]].directory, adr1 ∈ fs1

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)