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Proof step 93 from proof fsync-inode-keep-abs (previous step)

icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode = mkinode(m4, md1, false, m5, m6, m7), files[m0] = mkfile(m1, md0, m2, content), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), icache-cons(icache, dirs, files), ino ∈ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))], m ∈ icache, m0 ∈ files, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m7, md1, m5, (ino = m0 ⊃ mkfile(m3, md, m2, content);files[ino]).content ⊕ mkcontent(ino, pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 94:
icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files[m0] = mkfile(m1, md0, m2, content), icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino] = mkientry(boolvar, inode), inode = mkinode(m4, md1, false, m5, m6, m7), icache-cons(icache, dirs, files), ino ∈ files, m0 ∈ files, m ∈ icache, ino ∈ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))] ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m7, md1, m5, (ino = m0 ⊃ mkfile(m3, md, m2, content);files[ino]).content ⊕ mkcontent(ino, pcache))

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache [m, mkientry(false, mkinode(m0, md, false, m2, 0, m3)) ] [ino ], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino], boolvar, inode