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Proof step 39 from proof inv-iget (previous step)

(ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino0 ∈ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ino ∈ icache, icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino = ino0 ∧ (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].dirty ⊃ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino ∈ files ∧ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.nlink = files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nlink ∧ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.nsubdirs = 0 ∧ ¬ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode = (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino ∈ dirs ⊃ mkinode (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].meta, true, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nlink, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nsubdirs, dirs[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].size) ;mkinode (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino, files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].meta, false, files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].nlink, 0, files[icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode.ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode = mkinode(m3, md0, boolvar0, m4, m5, m6), (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino0 ∈ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ino ∈ icache, m3 = ino0 ∧ (icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].dirty ⊃ m3 ∈ files ∧ m4 = files[m3].nlink ∧ m5 = 0 ∧ ¬ boolvar0 ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0].inode = (m3 ∈ dirs ⊃ mkinode(m3, dirs[m3].meta, true, dirs[m3].nlink, dirs[m3].nsubdirs, dirs[m3].size) ;mkinode(m3, files[m3].meta, false, files[m3].nlink, 0, files[m3].size) ) )

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(m, md, boolvar, m0, m1, m2)) ] [ino0 ] .inode, m3, md0, 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[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0] .inode, m3, md0, boolvar0, m4, m5, m6