[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 10 from proof ubifs-log-nodups-add5 (previous step)

fo.inodes?, ro.inodes?, dups(log + adr0 ' + adr1 ' + adr2 ' + adr3 ' + adr4 '), fo ⊆ dom fi, ro ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]) ⊦ adr0 = adr1, adr0 = adr2, adr0 = adr3, adr0 = adr4, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, dups(log), inodekey(0) ∈ ri, adr0 ∈ fs, adr1 ∈ fs, adr2 ∈ fs, adr3 ∈ fs, adr4 ∈ fs, adr4 ∈ log, adr3 ∈ log

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 11:
ro.inodes?, fo.inodes?, dups(log + adr0 ' + adr1 ' + adr2 ' + adr3 ' + adr4 '), ro ⊆ dom ri, fo ⊆ dom fi, inodekey(0) ∈ ri → ri[inodekey(0)] ∈ fs ∧ node-closed(fs[ri[inodekey(0)]], ri, fs, ro), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ adr0 = adr4, adr0 = adr3, adr0 = adr2, adr0 = adr1, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, dups(log), adr3 ∈ log, adr4 ∈ log, adr4 ∈ fs, adr3 ∈ fs, adr2 ∈ fs, adr1 ∈ fs, adr0 ∈ fs, inodekey(0) ∈ ri

Rule argument

pos: left 7 terms: inodekey(0)

Additional information

Used terms: inodekey(0)