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Proof step 452 from proof inv-rename-dir-dentry (previous step)

(m7 = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m7, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), err = ESUCCESS, icache = icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))], entries0[str0] ≠ ROOT_INO, afs-cons (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md0 ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m7 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries0[str0], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [entries0[str0] ] .meta, true, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [entries0[str0] ] .nlink, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [entries0[str0] ] .nsubdirs, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [entries0[str0] ] .size), false ; err, icache); dcache_delete#(m7, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set# (m7, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ synced (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 453:
(m7 = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m7, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [entries0[str0] ] = mkdir(m, md4, m8, m9, entries1), err = ESUCCESS, icache = icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))], afs-cons(dirs0, files), afs-cons (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md0 ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ ⟪icache_set#(mkinode(entries0[str0], md4, true, m8, m9, m), false; err, icache); dcache_delete#(m7, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set# (m7, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ synced (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), entries0[str0] = ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs0 [m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0) ] [entries0[str0], dirs0 [m7, mkdir (m1, md2, # links(m7, dirs0), m4, entries0) ] [entries0[str0] ] .meta:= md0 ] [entries0[str0] ], m, md4, m8, m9, entries1]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0] ] .meta:= md0 ] [entries0[str0] ], m, md4, m8, m9, entries1