| size = LEB_SIZE ⊦ ⟪cache_format#(n, asynced0, size, md; cache_dirs, cache_files, cache_asynced, cache_icache, cache_dcache, cache_pcache; cache_sync, err)⟫ ( ( err = ESUCCESS → ⟨afs_format#(n, asynced0, size, md; afs_dirs; afs_files, afs_asynced, err0)⟩ ((afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)) ∧ err = err0)) ∧ ( err ≠ ESUCCESS → (∀ dirs, files, asynced. ⟨afs_format#(n, asynced0, size, md; afs_dirs; afs_files, afs_asynced, err0)⟩ (dirs = afs_dirs ∧ files = afs_files ∧ (asynced ↔ afs_asynced) ∧ err = err0)))) |
⊦ ⟪cache_format#(n, asynced0, LEB_SIZE, md; cache_dirs, cache_files, cache_asynced, cache_icache, cache_dcache, cache_pcache; cache_sync, err)⟫ ( ( err = ESUCCESS → ⟨afs_format#(n, asynced0, LEB_SIZE, md; afs_dirs; afs_files, afs_asynced, err0)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ dirs, files, asynced. ⟨afs_format#(n, asynced0, LEB_SIZE, md; afs_dirs; afs_files, afs_asynced, err0)⟩ (dirs = afs_dirs ∧ files = afs_files ∧ (asynced ↔ afs_asynced) ∧ err = err0))))