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

icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode = mkinode(m3, md1, false, m4, m5, m6), icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))], ino0 ∈ icache, ino ∈ icache, ino ∈ dirs, ino0 ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile(m6, md1, m4, files[ino0].content ⊕ mkcontent(ino0, pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0] = mkientry(boolvar0, inode), inode = mkinode(m3, md1, false, m4, m5, m6), ino0 ∈ files, ino ∈ dirs, ino ∈ icache, ino0 ∈ icache, ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))] ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile(m6, md1, m4, files[ino0].content ⊕ mkcontent(ino0, pcache))

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache [ino, mkientry(false, mkinode(m, md, true, m0, m1, m2)) ] [ino0 ], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0], boolvar0, inode