Proof step 27 from proof inv-writepage (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 28:

  # 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?))

Rule argument

Additional information

Used simplifier rules: ubifs-cons-reduce: ⊦ ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0) → ( ubifs-cons(fs1, ri1, ro1, fi1, fo1, log1) ↔ ¬ inodekey(0) ∈ ri1 ∧ (ro0.inodes? → ro1.inodes?) ∧ (fo0.inodes? → fo1.inodes?) ∧ (ro0 ⊆ dom ri0 → (∀ key. key ∈ ro1 → key ∈ ri1)) ∧ (fo0 ⊆ dom fi0 → (∀ key. key ∈ fo1 → key ∈ fi1)) ∧ (¬ dups(log0) → ¬ dups(log1)) ∧ (∀ key. ( key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ ( key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE)) → key ∈ ri1 → ri1[key] ∈ fs1 ∧ fs1[ri1[key]].key = key ∧ (key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro1 ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro1 ∧ fs1[ri1[inodekey(key.ino)]].directory) ∧ ( key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE)) ∧ (∀ adr. ( 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 ∈ log1 → adr ∈ fs1 ∧ ( fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?)));%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs → ¬ dups(log + adr0 '); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ dups(log); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ fo → key ∈ fi; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ ro → key ∈ ri; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)