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Proof step 109 from proof overwrite-write-page-dirty (previous step)

icache[ino0].inode = mkinode(m2, md0, false, m3, m4, m5), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ icache, ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ ino0 = ino, mkfile(m5, md0, m3, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile(m5, md0, m3, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 110:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), icache[ino0] = mkientry(boolvar, inode), inode = mkinode(m2, md0, false, m3, m4, m5), ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache ⊦ ino0 = ino, mkfile(m5, md0, m3, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile(m5, md0, m3, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]))

Rule argument

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

Additional information

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