[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 377 from proof inv-write_inode (previous step)

(key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]) = mkfile(m0, md0, m1, content), pcache[key] = mkpentry(boolvar, buf), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), synced(files, icache, pcache), synced(dirs, icache, pcache), key ∈ pcache, m ∈ files, ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]) ⊦ m ∈ icache, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Heuristic use patterns applied rule all left

And obtained the following new goals

Proof step 378:
(key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]) = mkfile(m0, md0, m1, content), pcache[key] = mkpentry(boolvar, buf), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files, key ∈ pcache, key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]) ⊦ m ∈ icache, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Rule argument

pos: left 9 terms: key abort: T discard: F computed: F

Additional information

Used terms: key