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Proof step 41 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 ⊦ 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 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(ino)]]).directory ∧ # (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 obtained the following new goals

Proof step 42:
# 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), ro.inodes?, fo.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(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, inodekey(ino) ∈ 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(m)]].directory, fs0[ri[inodekey(ino)]].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 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(ino)]]).directory ∧ # (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

Rule argument

fma: adr1 = ri[inodekey(ino)]

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss) Used formulas: adr1 = ri[inodekey(ino)]