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Proof step 196 from proof inv-rename-dir-negdentry (previous step)

(m = m9 ⊃ mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str);mkdir(m8, md5, # links(m, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries2), (m9 = m ⊃ mkdir(m4 + 1, md4, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)) = mkdir(m0, md1, m11, m12, entries1), (m = m9 ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])) = mkdir(m13, md6, m14, m15, entries4), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m10, entries3), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), afs-cons(dirs0, files), afs-cons (dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, m ∈ dirs0, str ∈ entries0, m9 ∈ dirs0, m = m9 → md4 = md0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO ⊦ dcache-cons ((dcache0 -- dentrykey(m9, str))[dentrykey(m, str0), mkdentry(str0, entries0[str])], dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files), str0 ∈ entries3

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 197:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))
Proof step 198:
(m = m9 ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])) = mkdir(m13, md6, m14, m15, entries4), (m9 = m ⊃ mkdir(m4 + 1, md4, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)) = mkdir(m0, md1, m11, m12, entries1), (m = m9 ⊃ mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str);mkdir(m8, md5, # links(m, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries2), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m10, entries3), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), afs-cons (dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files), afs-cons(dirs0, files), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), m9 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries0[str] ∈ dirs0, asynced2 → synced(files, icache0, pcache), m = m9 → md4 = md0, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries3, ∀ key. key ∈ (dcache0 -- dentrykey(m9, str))[dentrykey(m, str0), mkdentry(str0, entries0[str])] → key.dentry? ∧ key.name = (dcache0 -- dentrykey(m9, str))[dentrykey(m, str0), mkdentry(str0, entries0[str])][key].name ∧ valid-dentry (key.ino, (dcache0 -- dentrykey(m9, str))[dentrykey(m, str0), mkdentry(str0, entries0[str])][key], dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files)

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [(dcache0 -- dentrykey(m9, str) )[dentrykey(m, str0), mkdentry(str0, entries0[str]) ], dirs0 [m9, (m9 = m ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m9, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files] flags: <all paths>

Additional information

Used terms: (dcache0 -- dentrykey(m9, str) )[dentrykey(m, str0), mkdentry(str0, entries0[str]) ], dirs0 [m9, (m9 = m ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files