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Proof step 121 from proof inv-rmdir (previous step)

(entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][ino] = mkientry(true, inode0), icache0[ino] = mkientry(false, inode), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), afs-cons(dirs0, files), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), synced(files, icache0, pcache), ino ∈ icache0, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))], entries0[str] ∈ dirs0, str ∈ entries0, m5 ∈ dirs0, ino ∈ files, 1 ≤ m2, 1 ≤ m0, datakey(ino, n) ∈ pcache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, ino = m5, m0 = 0, m2 = 0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 122:
⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache
Proof step 123:
(m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), icache0[ino] = mkientry(false, inode), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][ino] = mkientry(true, inode0), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), afs-cons(dirs0, files), synced(files, icache0, pcache), ino ∈ files, m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, ino ∈ icache0, 1 ≤ m0, 1 ≤ m2, datakey(ino, n) ∈ pcache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO, ino = entries0[str] ∨ ino ∈ icache0 ⊦ entries0[str] = ROOT_INO, ino = m5, m0 = 0, m2 = 0

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, entries0[str], mkientry (false, mkinode(entries0[str], md0, true, m8, m9, m))] flags: <all paths>

Additional information

Used terms: ino, icache0, entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))