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Proof step 146 from proof inv-rename-file-dentry (previous step)

# links(entries1[str], dirs0) = m11 + 1, (m15 = m0 ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m15, dirs0), m7, entries -- str0)) = mkdir(m12, md7, m13, m14, entries2), (m0 = m15 ⊃ mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m0, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), dirs0[m0] = mkdir(m4, md4, # links(m0, dirs0), m8, entries1), files0[entries1[str]] = mkfile(m5, md5, m11 + 1, content1), files0[entries[str0]] = mkfile(m3, md0, # links(entries[str0], dirs0), content), dirs0[m15] = mkdir(m1 + 1, md6, # links(m15, dirs0), m7, entries), err = ESUCCESS, icache = icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))] [m0, mkientry (false, mkinode (m0, md1, true, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nlink, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nsubdirs, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).size)) ], afs-cons (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), entries1[str] ∈ files0, m0 ∈ dirs0, str ∈ entries1, m15 ∈ dirs0, entries[str0] ∈ files0, str0 ∈ entries, ¬ entries[str0] ∈ dirs0, ¬ entries1[str] ∈ dirs0, asynced2 → synced(files0, icache0, pcache), m0 = m15 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m15, dirs0) ≠ ∅ ∨ m15 = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries1[str], files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].meta, false, files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].nlink, 0, files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].size), false ; err, icache); dcache_delete#(m15, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set# (m0, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]) ∧ dcache-cons (dcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]) ∧ pcache-cons (pcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]) ∧ synced (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], icache, pcache) ∧ (asynced2 → synced(files0[entries1[str], mkfile(m2, md, m11, content1)], icache, pcache))), m15 = m0 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 147:
# links(entries1[str], dirs0) = m11 + 1, (m0 = m15 ⊃ mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m0, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), (m15 = m0 ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m15, dirs0), m7, entries -- str0)) = mkdir(m12, md7, m13, m14, entries2), dirs0[m15] = mkdir(m1 + 1, md6, # links(m15, dirs0), m7, entries), files0[entries[str0]] = mkfile(m3, md0, # links(entries[str0], dirs0), content), files0[entries1[str]] = mkfile(m5, md5, m11 + 1, content1), dirs0[m0] = mkdir(m4, md4, # links(m0, dirs0), m8, entries1), files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]] = mkfile(m, md8, m16, content0), err = ESUCCESS, icache = icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))] [m0, mkientry (false, mkinode (m0, md1, true, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nlink, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nsubdirs, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).size)) ], afs-cons(dirs0, files0), afs-cons (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), str0 ∈ entries, entries[str0] ∈ files0, m15 ∈ dirs0, str ∈ entries1, m0 ∈ dirs0, entries1[str] ∈ files0, m0 = m15 → md1 = md2, asynced2 → synced(files0, icache0, pcache), links(m15, dirs0) ≠ ∅ ∨ m15 = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set#(mkinode(entries1[str], md8, false, m16, 0, m), false; err, icache); dcache_delete#(m15, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set# (m0, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]) ∧ dcache-cons (dcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]) ∧ pcache-cons (pcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m2, md, m11, content1)]) ∧ synced (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], icache, pcache) ∧ (asynced2 → synced(files0[entries1[str], mkfile(m2, md, m11, content1)], icache, pcache))), entries[str0] ∈ dirs0, entries1[str] ∈ dirs0, m15 = m0 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files0 [entries1[str], ( files0 [entries1[str], mkfile(m5, md5, m11, content1) ] [entries1[str] ] .size:= m2) .meta:= md ] [entries1[str] ], m, md8, m16, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files0 [entries1[str], ( files0 [entries1[str], mkfile(m5, md5, m11, content1) ] [entries1[str] ] .size:= m2) .meta:= md ] [entries1[str] ], m, md8, m16, content0