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Proof step 152 from proof inv-rename-dir-dentry (previous step)

(m0 = m18 ⊃ mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0);mkdir(m4, md3, # links(m0, dirs0), m7, entries2)) = mkdir(m8, md6, m10, m11, entries1), (entries2[str] = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;(entries2[str] = m18 ⊃ mkdir(m1, md0, # links(entries2[str], dirs0), m2, entries0 -- str0) ;mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅) ) ) = mkdir(m13, md7, m12 + 1, m15, entries3), (m18 = entries2[str] ⊃ (entries2[str] = m0 ⊃ mkdir(m13, md1, m12, m15, entries3);mkdir(m13, md2, m12, m15, entries3)).meta:= md ;(m18 = m0 ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md2, # links(m18, dirs0), m2, entries0 -- str0)) ) = mkdir(m14, md8, m16, m17, entries4), (m0 = entries2[str] ⊃ (entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1.meta:= md ;(m0 = m18 ⊃ mkdir(m8, md2, m10, m11, entries1[str, entries0[str0]]);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md1 ) = mkdir(m, md9, m19, m20, entries5), dirs0[m18] = mkdir(m1 + 1, md0, # links(m18, dirs0), m2 + 1, entries0), dirs0[m0] = mkdir(m4, md3, # links(m0, dirs0), m7, entries2), dirs0[entries2[str]] = mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅), dirs0[entries0[str0]] = mkdir(m3, md4, # links(entries0[str0], dirs0), m5, entries), err = ESUCCESS, icache = icache0[m18, mkientry(false, mkinode(m18, md8, true, m16, m17, m14))][m0, mkientry(false, mkinode(m0, md9, true, m19, m20, m))], afs-cons(dirs0, files), afs-cons (dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], (entries2[str] = m0 ⊃ (entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, entries2[str] ∈ dirs0, str0 ∈ entries0, m18 ∈ dirs0, str ∈ entries2, m0 ∈ dirs0, m0 = m18 → md1 = md2, asynced2 → synced(files, icache0, pcache), links(m18, dirs0) ≠ ∅ ∨ m18 = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# (( entries2[str] ∈ dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] ⊃ mkinode (entries2[str], dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [entries2[str] ] .meta, true, dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [entries2[str] ] .nlink, dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [entries2[str] ] .nsubdirs, dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [entries2[str] ] .size) ;mkinode(entries2[str], files[entries2[str]].meta, false, files[entries2[str]].nlink, 0, files[entries2[str]].size) ), false ; err, icache); dcache_delete#(m18, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set# (m0, mkdentry(mkdentry(str, entries2[str]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str, entries2[str]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], (entries2[str] = m0 ⊃ (entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ], files) ∧ dcache-cons (dcache, dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], (entries2[str] = m0 ⊃ (entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ], files) ∧ pcache-cons (pcache, dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], (entries2[str] = m0 ⊃ (entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ], files) ∧ synced (dirs0 [m18, (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m18 = m0 ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m18, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m0, (m0 = m18 ⊃ (m18 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], (entries2[str] = m0 ⊃ (entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries2[str] = m18 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), entries2[str] = ROOT_INO, m18 = m0 ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries0[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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