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Proof step 398 from proof inv-rename-file-dentry (previous step)

dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), err = ESUCCESS, icache = icache0[m, mkientry(false, mkinode(m, md2, true, # links(m, dirs0), m4, m1))], afs-cons(dirs0, files), afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, ¬ entries[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries[str0], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].meta, false, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].nlink, 0, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].size), false ; err, icache); dcache_delete# ((m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .size) ) .ino, mkdentry(str0, entries[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .size) ) .ino, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ synced(dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], icache, pcache) ∧ (asynced2 → synced(files[entries[str0], (files[entries[str0]].size:= m2).meta:= md], icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 399:
(m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .size) ) = mkinode(m3, md3, boolvar, m5, m6, m7), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries), err = ESUCCESS, icache = icache0[m, mkientry(false, mkinode(m, md2, true, # links(m, dirs0), m4, m1))], afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries[str0], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].meta, false, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].nlink, 0, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].size), false ; err, icache); dcache_delete#(m3, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set# (m3, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ synced(dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], icache, pcache) ∧ (asynced2 → synced(files[entries[str0], (files[entries[str0]].size:= m2).meta:= md], icache, pcache))), entries[str0] ∈ dirs0

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] → [(m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ ( files[entries[str0]] .size:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .size) .meta:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ ( files[entries[str0]] .size:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .size) .meta:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ ( files[entries[str0]] .size:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .size) .meta:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .meta ;files[m] ) .size) ), m3, md3, boolvar, m5, m6, m7]

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: (m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ ( files[entries[str0]] .size:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .size) .meta:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ ( files[entries[str0]] .size:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .size) .meta:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ ( files[entries[str0]] .size:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .size) .meta:= mkinode (entries[str0], md, false, # links(entries[str0], dirs0), 0, m2) .meta ;files[m] ) .size) ), m3, md3, boolvar, m5, m6, m7