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Proof step 28 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, 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 ⊦ fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0, ( ( 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 → ((datakey(m, pageno) = key ⊃ adr1;ri[key]) = adr1 ∨ (datakey(m, pageno) = key ⊃ adr1;ri[key]) ∈ fs0) ∧ (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).key = key ∧ ( 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)) ∧ ( ( adr ∈ log0 → adr ∈ fs0 ∧ (fs0[adr].inode? → fs0[adr].key.inode? ∧ fs0[adr].key.ino ≠ 0) ∧ (fs0[adr].dentry? → fs0[adr].key.dentry?) ∧ (fs0[adr].data? → fs0[adr].key.data?) ∧ (fs0[adr].trunc? → fs0[adr].key.inode?)) → adr ∈ log0 ∨ adr = adr1 → (adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).inode? → (adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).key.inode? ∧ (adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).key.ino ≠ 0) ∧ ((adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).dentry? → (adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).key.dentry?) ∧ ((adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).data? → (adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).key.data?) ∧ ((adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).trunc? → (adr1 = adr ⊃ datanode(datakey(m, pageno), buf);fs0[adr]).key.inode?))

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 3

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