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Proof step 109 from proof fsync-inode-keep-abs (previous step)

icache[ino] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[m0] = mkfile(m1, md0, m2, content), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files[ino] = mkfile(m8, md2, m9, content0), icache-cons(icache, dirs, files), ino ∈ icache, m ∈ icache, m0 ∈ files, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m7, md1, m5, content0 ⊕ mkcontent(ino, pcache)), ino = m, ino = m0

User applied rule insert rewrite lemma

And obtained the following new goals

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, icache, files ⊕ pcache] 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)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s) Used terms: ino, icache, files ⊕ pcache