[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 153 from proof ubifs-cons-reduce (previous step)

ro0.inodes?, fo0.inodes?, log-cons(log0, fs0), ri-closed(ri0, fs0, ro0), ri-cons(ri0, fs0), key ∈ ro1, ro0 ⊆ dom ri0, fo0 ⊆ dom fi0, ∀ adr. ( adr ∈ log0 → (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?), ∀ key. ( key ∈ ri0 → 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), ∀ key. key ∈ fo1 → key ∈ fi1, ∀ key. key ∈ ro1 → key ∈ ri1 ⊦ # ro1 = 0, ro1 = ∅, dups(log0), inodekey(0) ∈ ri1, key ∈ ri1, inodekey(0) ∈ ri0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 154:
fo0.inodes?, ro0.inodes?, log-cons(log0, fs0), ri-closed(ri0, fs0, ro0), ri-cons(ri0, fs0), key ∈ ro1, fo0 ⊆ dom fi0, ro0 ⊆ dom ri0, ∀ key. key ∈ ro1 → key ∈ ri1, ∀ key. key ∈ fo1 → key ∈ fi1, ∀ adr. ( adr ∈ log0 → (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?), ∀ key0. ( key0 ∈ ri0 → (key0.inode? → fs0[ri0[key0]].inode? ∧ key0.ino ≠ 0) ∧ ( key0.dentry? → fs0[ri0[key0]].dentry? ∧ inodekey(key0.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key0]].ino) ∈ ri0 ∧ ¬ inodekey(key0.ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key0]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(key0.ino)]].directory) ∧ ( key0.data? → fs0[ri0[key0]].data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key0.ino)]].directory ∧ # fs0[ri0[key0]].data = VFS_PAGE_SIZE)) → key0 ∈ ri1 → ri1[key0] ∈ fs1 ∧ fs1[ri1[key0]].key = key0 ∧ (key0.inode? → fs1[ri1[key0]].inode? ∧ key0.ino ≠ 0) ∧ ( key0.dentry? → fs1[ri1[key0]].dentry? ∧ inodekey(key0.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key0]].ino) ∈ ri1 ∧ ¬ inodekey(key0.ino) ∈ ro1 ∧ ¬ inodekey(fs1[ri1[key0]].ino) ∈ ro1 ∧ fs1[ri1[inodekey(key0.ino)]].directory) ∧ ( key0.data? → fs1[ri1[key0]].data? ∧ inodekey(key0.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key0.ino)]].directory ∧ # fs1[ri1[key0]].data = VFS_PAGE_SIZE) ⊦ # ro1 = 0, ro1 = ∅, dups(log0), inodekey(0) ∈ ri0, key ∈ ri1, inodekey(0) ∈ ri1

Rule argument

Additional information

Used simplifier rules: ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (s)