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Proof step 27 from proof overwrite-write-inode-clean-dir (previous step)

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 (icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode.size, icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode.meta, icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode.nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)), icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0].inode = mkinode(m3, md1, boolvar0, m4, m5, m6), icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), ¬ boolvar0, 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: 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 [ino, mkientry(false, mkinode(m, md, true, m0, m1, m2)) ] [ino0 ] .inode, m3, md1, boolvar0, m4, m5, m6]

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[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0] .inode, m3, md1, boolvar0, m4, m5, m6