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Proof step 134 from proof fsync-inode-inv (previous step)

icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), dirs[m1] = mkdir(m7, md2, m8, m9, entries), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))], m ∈ files, m ∈ icache, m1 ∈ files ⊦ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = ino ∧ (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].dirty ⊃ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino ∈ files ∧ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.nlink = (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino] ) .nlink ∧ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode = (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].meta, true, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].nlink, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].nsubdirs, dirs[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino].size) ;mkinode (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino, (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino] ) .meta, false, (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino] ) .nlink, 0, (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0) ;files[icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode.ino] ) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 135:
icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode = mkinode(m2, md3, boolvar, m3, m6, m10), files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), dirs[m1] = mkdir(m7, md2, m8, m9, entries), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m1 ∈ files, m ∈ icache, m ∈ files, ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))] ⊦ m2 = ino ∧ (icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].dirty ⊃ m2 ∈ files ∧ m3 = (m2 = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[m2]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].inode = (m2 ∈ dirs ⊃ mkinode(m2, dirs[m2].meta, true, dirs[m2].nlink, dirs[m2].nsubdirs, dirs[m2].size) ;mkinode (m2, (m2 = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[m2]).meta, false, (m2 = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[m2]).nlink, 0, (m2 = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[m2]).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(m1, md, false, # links(m1, dirs), 0, m4)) ] [ino ] .inode, m2, md3, boolvar, m3, m6, m10]

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(m1, md, false, # links(m1, dirs), 0, m4)) ] [ino ] .inode, m2, md3, boolvar, m3, m6, m10