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Proof step 77 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, asynced ↔ false, files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), err = ESUCCESS, icache = icache0[inode.ino, mkientry(asynced, inode)], inode = getinode (entries0[str], dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= m3).meta:= md0]), 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), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# ((m0 ∈ dirs0 ⊃ mkinode(m0, md3, true, # links(m0, dirs0), m7, m8) ;mkinode (m0, (m0 = 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)][m0] ) .meta, false, (m0 = 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)][m0] ) .nlink, 0, (m0 = 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)][m0] ) .size) ), false ; err, icache); dcache_delete#(m0, mkdentry(str, entries0[str]).name; err, dcache)⟫ ( icache-cons (icache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ dcache-cons (dcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ pcache-cons (pcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ synced(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], icache, pcache) ∧ (asynced1 → synced(files0[entries0[str], mkfile(m3, md0, m2, content0)], icache, pcache)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
# links(entries0[str], dirs0) = m2 + 1, files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), err = ESUCCESS, icache = icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))], 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), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set#(mkinode(m0, md3, true, # links(m0, dirs0), m7, m8), false; err, icache); dcache_delete#(m0, mkdentry(str, entries0[str]).name; err, dcache)⟫ ( icache-cons (icache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ dcache-cons (dcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ pcache-cons (pcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ synced(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], icache, pcache) ∧ (asynced1 → synced(files0[entries0[str], mkfile(m3, md0, m2, content0)], icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)