[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 204 from proof fsync-others-unchanged (previous step)

files0[ino] = mkfile(m2, md1, # links(ino, dirs), content2), files1[ino] = mkfile(m2, md1, # links(ino, dirs), content1), files1[m] = mkfile(m1, md, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), content1 ⊕ mkcontent(ino, pcache1) = content2 ⊕ mkcontent(ino, pcache0), afs-cons(dirs, files0), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files1), icache-cons(icache0, dirs, files0), icache-cons(icache0, dirs, files1), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache1, dirs, files1), synced(dirs, icache0, pcache0), synced(dirs, icache0, pcache1), ino ∈ files0, m ∈ files0, m ∈ files1, ino ∈ files1, ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files1 ∧ mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache1)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ⊦ ((files1 ⊕ pcache1) ⊕ icache0)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], err0 = ESUCCESS, ino = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 205:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 206:
files0[m] = mkfile(m0, md0, # links(m, dirs), content), files1[m] = mkfile(m1, md, # links(m, dirs), content0), files1[ino] = mkfile(m2, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m2, md1, # links(ino, dirs), content2), content1 ⊕ mkcontent(ino, pcache1) = content2 ⊕ mkcontent(ino, pcache0), afs-cons(dirs, files1), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files1), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files1), icache-cons(icache0, dirs, files0), pcache-cons(pcache1, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache1), synced(dirs, icache0, pcache0), ino ∈ files1, m ∈ files1, m ∈ files0, ino ∈ files0, ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files1 ∧ mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache1)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ⊦ ((files1 ⊕ pcache1) ⊕ icache0)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], err0 = ESUCCESS, ino = m, ino ∈ icache0 ∧ icache0[ino].inode.directory

Rule argument

spec: cache-base name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [ino, icache0, files1 ⊕ pcache1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s) Used terms: ino, icache0, files1 ⊕ pcache1