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Proof step 126 from proof fsync-others-unchanged (previous step)

files[ino] = mkfile(m7, md3, m8, content3), 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), (∅)[ino] = mkientry(boolvar0, mkinode(m3, md2, boolvar, m4, m5, m6)), mkfile(m7, md3, m8, content3) = (files1 ⊕ icache0)[ino], 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 ⊦ err = ESUCCESS, ino = m, mkfile(m7, md3, m8, content3 ⊕ mkcontent(ino, pcache1)) = ((files0 ⊕ pcache0) ⊕ icache0)[ino], ino ∈ icache1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 127:
⊦ 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 128:
(∅)[ino] = mkientry(boolvar0, mkinode(m3, md2, boolvar, m4, m5, m6)), 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[ino] = mkfile(m7, md3, m8, content3), mkfile(m7, md3, m8, content3) = (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 ⊦ err = ESUCCESS, ino = m, mkfile(m7, md3, m8, content3 ⊕ mkcontent(ino, pcache1)) = ((files0 ⊕ pcache0) ⊕ icache0)[ino], ino ∈ icache1, ino ∈ icache0 ∧ ¬ icache0[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, icache0, files0 ⊕ pcache0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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); (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s) Used terms: ino, icache0, files0 ⊕ pcache0