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Proof step 26 from proof overwrite-write-inode-dirty (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 27:
icache[ino] = mkientry(boolvar, inode), icache[ino0] = mkientry(boolvar0, inode0), inode0 = mkinode(m0, md0, true, m1, m2, m3), ino0 ∈ icache, ino0 ∈ files, ino ∈ files, ino ∈ icache ⊦ ino0 = ino, mkfile(files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)) = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino0], inode.directory

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino0], boolvar0, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino0], boolvar0, inode0