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Proof step 567 from proof inv-rename-dir-dentry (previous step)

icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))][ino] .inode = mkinode(m10, md5, boolvar, m11, m12, m13), (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md0 = mkdir(m, md4, m8, m9, entries1), (m7 = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m7, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), afs-cons(dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files), afs-cons(dirs0, files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), m7 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, ino ∈ icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))], asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, m10 = ino ∧ (icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))] [ino ] .dirty ⊃ ino ∈ files ∧ m11 = files[ino].nlink ∧ m12 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md5, boolvar, m11, m12, m13) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).meta, true, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nlink, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nsubdirs, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 568:
(entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md0 = mkdir(m, md4, m8, m9, entries1), (m7 = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m7, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))][ino] = mkientry(boolvar0, inode), inode = mkinode(m10, md5, boolvar, m11, m12, m13), afs-cons(dirs0, files), afs-cons(dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), ino ∈ icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))], entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, m10 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m11 = files[ino].nlink ∧ m12 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md5, boolvar, m11, m12, m13) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).meta, true, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nlink, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nsubdirs, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache0 [m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0)) ] [entries0[str0], mkientry (false, mkinode(entries0[str0], md4, true, m8, m9, m)) ] [ino ], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m)) ] [ino ], boolvar0, inode