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Proof step 186 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), icache-cons(icache0, dirs0, files0), synced(dirs0, icache0, pcache), ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = ino ∧ (icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .dirty ⊃ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ∈ files0 ∧ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .nlink = ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0) ;files0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .nlink ∧ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .nsubdirs = 0 ∧ ¬ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .directory ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode = ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ∈ dirs0 ⊃ mkinode (icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino, ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str) ;dirs0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .meta, true, ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str) ;dirs0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .nlink, ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str) ;dirs0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .nsubdirs, ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str) ;dirs0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .size) ;mkinode (icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino, ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0) ;files0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .meta, false, ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0) ;files0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .nlink, 0, ( icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0) ;files0 [icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode .ino ] ) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 187:
# links(entries0[str], dirs0) = m2 + 1, icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode = mkinode(m, md, boolvar, m4, m5, m6), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), icache-cons(icache0, dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m = ino ∧ (icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .dirty ⊃ m ∈ files0 ∧ m4 = (m = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[m]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode = (m ∈ dirs0 ⊃ mkinode (m, (m = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[m]).meta, true, (m = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[m]).nlink, (m = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[m]).nsubdirs, (m = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[m]).size) ;mkinode (m, (m = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[m]).meta, false, (m = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[m]).nlink, 0, (m = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[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 [entries0[str], mkientry (false, mkinode(entries0[str], md0, false, m2, 0, m3)) ] [m0, mkientry (false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode, m, md, boolvar, 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: icache0 [entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3)) ] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .inode, m, md, boolvar, m4, m5, m6