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Proof step 31 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, 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, 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, ((datakey(m, pageno) = key ⊃ adr1;ri[key]) = adr1 ∨ (datakey(m, pageno) = key ⊃ adr1;ri[key]) ∈ fs0) ∧ ( key.inode? → (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).dentry? ∧ inodekey(key.ino) ∈ ri ∧ inodekey ((adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).ino) ∈ ro ∧ (adr1 = ri[inodekey(key.ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(key.ino)]]).directory) ∧ ( key.data? → (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 if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 32:
# 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.dentry?, 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])]).dentry? ∧ inodekey(key.ino) ∈ ri ∧ inodekey ((adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).ino) ∈ ro ∧ (adr1 = ri[inodekey(key.ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(key.ino)]]).directory
Proof step 36:
# 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

Rule argument

pos: right 3

Additional information

Used simplifier rules: elim-inode: ⊦ key.inode? ↔ (∃ ino. key = inodekey(ino));%inode-ubifs-cons: ⊦ inodekey(ino) ∈ ri ∧ ri[inodekey(ino)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].inode?;% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ ¬ inodekey(m).dentry?; (s)% ⊦ ¬ inodekey(m).data?; (s)% ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)% ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss)