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Proof step 190 from proof inv-mkdir (previous step)

icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode = mkinode(m, md0, boolvar, m1, m2, m4), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), afs-cons(dirs0, files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, ino ∈ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ], asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino0 = 0, str ∈ entries0, ino0 ∈ files, ino0 ∈ dirs0, m = ino ∧ (icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .dirty ⊃ ino ∈ files ∧ m1 = files[ino].nlink ∧ m2 = 0 ∧ ¬ boolvar ; (ino = ino0 ∨ ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m1, m2, m4) = (ino = ino0 ∨ ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .meta, true, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nlink, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nsubdirs, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 191:
dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] = mkientry(boolvar0, inode), inode = mkinode(m, md0, boolvar, m1, m2, m4), afs-cons(dirs0, files), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), ino ∈ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ], m0 ∈ dirs0, asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0, m = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m1 = files[ino].nlink ∧ m2 = 0 ∧ ¬ boolvar ; (ino = ino0 ∨ ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m1, m2, m4) = (ino = ino0 ∨ ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .meta, true, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nlink, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nsubdirs, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache0 [m0, mkientry (false, mkinode (m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache0 [m0, mkientry (false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ], boolvar0, inode