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Proof step 43 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, (adr1 = (datakey(m, pageno) = datakey(ino, n) ⊃ adr1;ri[datakey(ino, n)]) ⊃ datanode(datakey(m, pageno), buf) ;fs0[(datakey(m, pageno) = datakey(ino, n) ⊃ adr1;ri[datakey(ino, n)])] ) .key = datakey(ino, n), fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(ino) ∈ ri, inodekey(m) ∈ ri, datakey(ino, n) ∈ ri → ri[datakey(ino, n)] ∈ fs0 ∧ fs0[ri[datakey(ino, n)]].key = datakey(ino, n) ∧ fs0[ri[datakey(ino, n)]].data?, datakey(ino, n) = datakey(m, pageno) ∨ datakey(ino, n) ∈ ri ⊦ adr1 = ri[inodekey(ino)], fs0[ri[inodekey(ino)]].directory, fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0, (adr1 = (datakey(m, pageno) = datakey(ino, n) ⊃ adr1;ri[datakey(ino, n)]) ⊃ datanode(datakey(m, pageno), buf) ;fs0[(datakey(m, pageno) = datakey(ino, n) ⊃ adr1;ri[datakey(ino, n)])] ) .data? ∧ # (adr1 = (datakey(m, pageno) = datakey(ino, n) ⊃ adr1;ri[datakey(ino, n)]) ⊃ datanode(datakey(m, pageno), buf) ;fs0[(datakey(m, pageno) = datakey(ino, n) ⊃ adr1;ri[datakey(ino, n)])] ) .data = VFS_PAGE_SIZE

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: adr1 = (datakey(m, pageno) = datakey(ino, n) ⊃ adr1 ;ri[datakey(ino, n)] )

Additional information

Used simplifier rules: data-ubifs-cons: ⊦ datakey(ino, n) ∈ ri ∧ ri[datakey(ino, n)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[datakey(ino, n)]].data?;% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ datanode(key, buf).key = key; (s)% ⊦ datanode(key, buf).data?; (s)% ⊦ datanode(key, buf).data = buf; (s) Used formulas: adr1 = (datakey(m, pageno) = datakey(ino, n) ⊃ adr1;ri[datakey(ino, n)])