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Proof step 174 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), icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][ino] = mkientry(true, inode0), icache0[ino] = mkientry(false, inode), 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), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), 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), synced(dirs0, icache0, pcache), ino ∈ icache0, ino ∈ icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))], ino ∈ dirs0, entries0[str] ∈ dirs0, m ∈ dirs0, str ∈ entries0, m9 ∈ dirs0, m = m9 → md4 = md0, asynced2 → synced(files, icache0, pcache), datakey(ino, n) ∈ pcache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO ⊦ ino = m, str0 ∈ entries3

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 175:
⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache
Proof step 176:
(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), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), 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), icache0[ino] = mkientry(false, inode), icache0[m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))][ino] = mkientry(true, inode0), 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), synced(dirs0, icache0, pcache), m9 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries0[str] ∈ dirs0, ino ∈ dirs0, ino ∈ icache0, datakey(ino, n) ∈ pcache → ¬ boolvar, asynced2 → synced(files, icache0, pcache), m = m9 → md4 = md0, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, ino = m9 ∨ ino ∈ icache0 ⊦ ino = m, str0 ∈ entries3

Rule argument

spec: store, inst: icache name: In-insert seq: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache subst: [ino, icache, ino0, ie] → [ino, icache0, m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))] flags: <all paths>

Additional information

Used terms: ino, icache0, m9, mkientry(false, mkinode(m9, md1, true, m11, m12, m0))