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Proof step 539 from proof inv-rename-dir-dentry (previous step)

(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), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], m7 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, key.dentry? ∧ key.name = dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∧ key.ino ∈ dirs0 ∧ ( links(key.ino, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)]) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∈ (key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);dirs0[key.ino]) ) .entries ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino = (key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);dirs0[key.ino]) ) .entries [dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ] ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].dentry?

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 540:
(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), (key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);dirs0[key.ino]) ) = mkdir(m10, md5, m11, m12, entries2), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), 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), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, key.dentry? ∧ key.name = dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∧ key.ino ∈ dirs0 ∧ ( links(key.ino, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)]) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∈ entries2 ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino = entries2[dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name] ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].dentry?

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [(key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0) ;dirs0[key.ino] ) ), m10, md5, m11, m12, entries2]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: (key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0) ;dirs0[key.ino] ) ), m10, md5, m11, m12, entries2