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Proof step 18 from proof overwrite-write-page-clean (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, inode), inode = mkinode(m0, md, true, m1, m4, m5), ino ∈ files, ino ∈ icache ⊦ mkfile(m2, md0, m3, (content0 ⊕ mkcontent(ino, pcache))[m, buf]) = mkfile(m2, md0, m3, content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))

Rule argument

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

Additional information

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