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Proof step 72 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m4, entries0), err = ESUCCESS, m0 = m5 + 1, afs-cons(dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, 1 ≤ m0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (getinode (entries0[str], dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= m3).meta:= md0]), false ; err, icache); icache_set# ((m ∈ dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)] ⊃ mkinode (m, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)][m].meta, true, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)][m].nlink, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)][m].nsubdirs, dirs0[m, mkdir(m5, 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) ), false ; err, icache); dcache_delete# ((m ∈ dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)] ⊃ mkinode (m, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)][m].meta, true, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)][m].nlink, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)][m].nsubdirs, dirs0[m, mkdir(m5, 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(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ dcache-cons(dcache, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ pcache-cons(pcache, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ synced(dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], icache, pcache) ∧ (asynced1 → synced(files0[entries0[str], mkfile(m3, md0, m2, content0)], icache, pcache))), m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
# links(entries0[str], dirs0) = m2 + 1, dirs0[m] = mkdir(m5 + 1, md2, # links(m, dirs0), m4, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), err = ESUCCESS, afs-cons(dirs0, files0), afs-cons(dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), 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, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (getinode (entries0[str], dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= m3).meta:= md0]), false ; err, icache); icache_set# ((m ∈ dirs0 ⊃ mkinode(m, md, true, # links(m, dirs0), m4, m5) ;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) ), false ; err, icache); dcache_delete# ((m ∈ dirs0 ⊃ mkinode(m, md, true, # links(m, dirs0), m4, m5) ;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(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ dcache-cons(dcache, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ pcache-cons(pcache, dirs0[m, mkdir(m5, md, # links(m, dirs0), m4, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ synced(dirs0[m, mkdir(m5, 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: ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)