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Proof step 91 from proof fsync-inode-keep-abs (previous step)

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 (icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.size, icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.meta, icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.nlink, (ino = m0 ⊃ mkfile(m3, md, m2, content);files[ino]).content ⊕ mkcontent(ino, pcache)), icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 92:
icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode = mkinode(m4, md1, boolvar, m5, m6, m7), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files[m0] = mkfile(m1, md0, m2, content), ¬ boolvar, 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: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache [m, mkientry(false, mkinode(m0, md, false, m2, 0, m3)) ] [ino ] .inode, m4, md1, boolvar, m5, m6, m7]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino] .inode, m4, md1, boolvar, m5, m6, m7