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Proof step 78 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, ino = m, 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(ino) ∈ ri, inodekey(m) ∈ ri, asynced0 → boolvar0 ⊦ adr1 = ri[inodekey(ino)], 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[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])), fs1[ri[inodekey(ino)]].directory, fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
# 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 ⊦ adr1 = ri[inodekey(m)], fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1, (n ∈ abs-content(m, fs1, ri)[pageno, buf] ↔ datakey(m, n) ∈ ri[datakey(m, pageno), adr1]) ∧ ( n ∈ abs-content(m, fs1, ri)[pageno, buf] → abs-content(m, fs1, ri)[pageno, buf][n] = (adr1 = (datakey(m, pageno) = datakey(m, n) ⊃ adr1;ri[datakey(m, n)]) ⊃ datanode(datakey(m, pageno), buf) ;fs1[(datakey(m, pageno) = datakey(m, n) ⊃ adr1;ri[datakey(m, n)])] ) .data)

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)%⊦ content = abs-content(ino, fs, ri) ↔ (∀ n. (n ∈ content ↔ datakey(ino, n) ∈ ri) ∧ (n ∈ content → content[n] = fs[ri[datakey(ino, n)]].data)); (ss)%⊦ mkfile(m0, md0, n0, content0) = mkfile(m1, md1, n1, content1) ↔ ¬(n0 ≠ n1 ∨ md0 ≠ md1 ∨ m0 ≠ m1 ∨ content0 ≠ content1); (ss)