[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 3 from proof inv-recover (previous step)

dirs = dirs0 \ orphans(dirs0, files), files0 = files \ orphans(dirs0, files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), asynced0 → synced(files, icache, pcache) ⊦ ⟪cache_recovery#(asynced1; dirs, files0, asynced2, icache0, dcache0, pcache0; asynced3, err)⟫ ( err = ESUCCESS → asynced2 ∧ icache-cons(icache0, dirs, files0) ∧ dcache-cons(dcache0, dirs, files0) ∧ pcache-cons(pcache0, dirs, files0) ∧ synced(dirs, icache0, pcache0) ∧ (asynced3 → synced(files0, icache0, pcache0)) ∧ afs-cons(dirs, files0))

User applied rule call right

And obtained the following new goals

Proof step 4:
asynced0 ↔ asynced2, dcache = dcache0, dirs = dirs0 \ orphans(dirs0, files1), files = files0, files0 = files1 \ orphans(dirs0, files1), icache = icache0, pcache = pcache0, afs-cons(dirs0, files1), dcache-cons(dcache1, dirs0, files1), icache-cons(icache1, dirs0, files1), pcache-cons(pcache1, dirs0, files1), synced(dirs0, icache1, pcache1), asynced4 → synced(files1, icache1, pcache1) ⊦ ⟪asynced := asynced1; afs_recovery#(asynced1; dirs, files; asynced0, err); if err = ESUCCESS then icache_recovery#(; ; icache, err); if err = ESUCCESS then dcache_recovery#(; ; dcache, err); if err = ESUCCESS then pcache_recovery#(; ; pcache, err)⟫ ( err = ESUCCESS → asynced0 ∧ icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Rule argument

pos: right 1

Additional information

Used simplifier rules: recover: ⊦ ;