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Proof step 582 from proof overwrite-write-page-clean (previous step)

icache[ino0].inode = mkinode(m0, md, false, m1, m4, m5), files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ mkfile(m5, md, m1, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile(m5, md, m1, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])), ino ∈ icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 583:
files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, inode), inode = mkinode(m0, md, false, m1, m4, m5), ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ mkfile(m5, md, m1, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile(m5, md, m1, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])), ino ∈ icache

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