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Proof step 114 from proof fsync-others-unchanged (previous step)

files0[ino] = mkfile(m2, md, # links(ino, dirs), content2), files1[ino] = mkfile(m2, md, # links(ino, dirs), content1), files0[m] = mkfile(m0, md0, # links(m, dirs), content), files1[m] = mkfile(m1, md1, # links(m, dirs), content0), (files ⊕ icache1)[ino] = (files1 ⊕ icache0)[ino], 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 ∈ files ⊦ ((files ⊕ pcache1) ⊕ icache1)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], err = ESUCCESS, ino = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 115:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 116:
(files ⊕ icache1)[ino] = (files1 ⊕ icache0)[ino], files1[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), files1[ino] = mkfile(m2, md, # links(ino, dirs), content1), files0[ino] = mkfile(m2, md, # 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 ∈ files, ino ∈ files1, m ∈ files1, m ∈ files0, ino ∈ files0 ⊦ ((files ⊕ pcache1) ⊕ icache1)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino], err = ESUCCESS, ino = m, ino ∈ icache1 ∧ ¬ icache1[ino].inode.directory
Proof step 147:
(files ⊕ icache1)[ino] = (files1 ⊕ icache0)[ino], files1[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), files1[ino] = mkfile(m2, md, # links(ino, dirs), content1), files0[ino] = mkfile(m2, md, # 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 ∈ files, ino ∈ files1, m ∈ files1, m ∈ files0, ino ∈ files0, ino ∈ icache1 ⊦ err = ESUCCESS, ino = m, mkfile(icache1[ino].inode.size, icache1[ino].inode.meta, icache1[ino].inode.nlink, (files ⊕ pcache1)[ino].content) = ((files0 ⊕ pcache0) ⊕ icache0)[ino], icache1[ino].inode.directory

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [ino, icache1, files ⊕ pcache1] flags: <all paths>

Additional information

Used terms: ino, icache1, files ⊕ pcache1