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Proof step 66 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m4, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs = dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], files = files0[entries0[str], mkfile(m1, md1, m2, content0)], ino = inode.ino, inode = mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), str ∈ entries0, entries0[str] ∈ files0, m ∈ dirs0, ino ∈ files, 1 ≤ m0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [asynced := ?] ( afs-cons(dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) → ⟪if ESUCCESS = ESUCCESS then let asynced = false in {err := ESUCCESS; icache_set# (getinode (entries0[str], dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]), asynced ; err, icache); icache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ), asynced ; err, icache); dcache_delete# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache)}⟫ ( icache-cons (icache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ dcache-cons (dcache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ pcache-cons (pcache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ ( asynced1 → synced (files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta], icache, pcache)))), m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
# links(entries0[str], dirs0) = m2 + 1, dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m4, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), m0 ≠ 0, afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), str ∈ entries0, entries0[str] ∈ files0, m ∈ dirs0, 1 ≤ m0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [asynced := ?] ( afs-cons(dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) → ⟪let asynced = false in {err := ESUCCESS; icache_set# (getinode (entries0[str], dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], files0 [entries0[str], (entries0[str] ∈ files0 ⊃ files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] .size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size ;files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] ) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ]), asynced ; err, icache); icache_set# ((m ∈ dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)] ⊃ mkinode (m, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].meta, true, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].nlink, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].nsubdirs, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].size) ;mkinode (m, (m = entries0[str] ∧ entries0[str] ∈ files0 ⊃ ( files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] .size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m] ) .meta, false, (m = entries0[str] ∧ entries0[str] ∈ files0 ⊃ ( files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] .size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m] ) .nlink, 0, (m = entries0[str] ∧ entries0[str] ∈ files0 ⊃ ( files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] .size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m] ) .size) ), asynced ; err, icache); dcache_delete# ((m ∈ dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)] ⊃ mkinode (m, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].meta, true, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].nlink, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].nsubdirs, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)][m].size) ;mkinode (m, (m = entries0[str] ∧ entries0[str] ∈ files0 ⊃ ( files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] .size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m] ) .meta, false, (m = entries0[str] ∧ entries0[str] ∈ files0 ⊃ ( files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] .size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m] ) .nlink, 0, (m = entries0[str] ∧ entries0[str] ∈ files0 ⊃ ( files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]] .size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m] ) .size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache)}⟫ ( icache-cons (icache, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ synced(dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], icache, pcache) ∧ (asynced1 → synced(files0[entries0[str], mkfile(m3, md0, m2, content0)], icache, pcache))))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)