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Proof step 161 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), icache-cons(icache0, dirs0, files0), synced(dirs0, icache0, pcache), ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))], m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = ino ∧ (icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .dirty ⊃ ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ∨ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ∈ files0) ∧ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .nlink = ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0 )[icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .nlink ∧ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .nsubdirs = 0 ∧ ¬ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .directory ; (ino ∈ dirs0 ∨ ino = ino0 ∨ ino ∈ files0) ∧ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode = ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ∈ dirs0 ⊃ mkinode (icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino, ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ;dirs0 [icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .meta, true, ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ;dirs0 [icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .nlink, ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ;dirs0 [icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .nsubdirs, ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ;dirs0 [icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .size) ;mkinode (icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino, ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0 )[icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .meta, false, ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0 )[icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .nlink, 0, ( icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkfile(0, md, 1, ∅) ;(files0 ++ ino0 )[icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode .ino ] ) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 162:
icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))] [ino ] .inode = mkinode(m, md0, boolvar, m2, m3, m5), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), icache-cons(icache0, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))], asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, m = ino ∧ (icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .dirty ⊃ (m = ino0 ∨ m ∈ files0) ∧ m2 = (m = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino = ino0 ∨ ino ∈ files0) ∧ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode = (m ∈ dirs0 ⊃ mkinode (m, (m = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[m]).meta, true, (m = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[m]).nlink, (m = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[m]).nsubdirs, (m = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[m]).size) ;mkinode (m, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).meta, false, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).nlink, 0, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).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] → [icache0 [m1, mkientry (false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode, m, md0, boolvar, m2, m3, m5]

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: icache0 [m1, mkientry (false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] [ino ] .inode, m, md0, boolvar, m2, m3, m5