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Proof step 36 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).key = key, key.data?, 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(m) ∈ ri, key ∈ ri → ri[key] ∈ fs0 ∧ fs0[ri[key]].key = key ∧ (key.inode? → fs0[ri[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri[key]].dentry? ∧ inodekey(key.ino) ∈ ri ∧ inodekey(fs0[ri[key]].ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri[key]].ino) ∈ ro ∧ fs0[ri[inodekey(key.ino)]].directory) ∧ (key.data? → fs0[ri[key]].data? ∧ inodekey(key.ino) ∈ ri ∧ ¬ fs0[ri[inodekey(key.ino)]].directory ∧ # fs0[ri[key]].data = VFS_PAGE_SIZE), key = datakey(m, pageno) ∨ key ∈ ri ⊦ fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0, (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).data? ∧ inodekey(key.ino) ∈ ri ∧ ¬ (adr1 = ri[inodekey(key.ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(key.ino)]]).directory ∧ # (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).data = VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# 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(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? ∧ inodekey(ino) ∈ ri ∧ ¬ fs0[ri[inodekey(ino)]].directory, datakey(ino, n) = datakey(m, pageno) ∨ datakey(ino, n) ∈ ri ⊦ 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? ∧ inodekey(ino) ∈ ri ∧ ¬ (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

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ ¬ datakey(m, m0).dentry?; (s)% ⊦ ¬ datakey(m, m0).inode?; (s)