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Proof step 29 from proof overwrite-write-inode-dirty (previous step)

icache[ino] = mkientry(boolvar, inode), icache[ino0] = mkientry(boolvar0, mkinode(m0, md0, true, m1, m2, m3)), files[ino0] = mkfile(m4, md1, m5, content), ino0 ∈ icache, ino0 ∈ files, ino ∈ files, ino ∈ icache ⊦ ino0 = ino, mkfile(m4, md1, m5, content ⊕ mkcontent(ino0, pcache)) = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino0], inode.directory

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [ino0, icache[ino, mkientry(true, (inode.meta:= md).size:= m)], files ⊕ pcache] flags: <all paths>

Additional information

Used simplifier rules: at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[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)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s) Used terms: ino0, icache[ino, mkientry(true, (inode.meta:= md).size:= m)], files ⊕ pcache