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Proof step 125 from proof afs-cons-rename-dir-negdentry (previous step)

(ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]])).meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) ) = mkdir(m15, md7, m16, m17, entries4), (m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str);mkdir(m8, md5, # links(m0, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries0), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), files[ino] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), dirs0[m0] = mkdir(m8, md5, # links(m0, dirs0), m10, entries3), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries2, entries2[str] ∈ dirs0, m0 ∈ dirs0, ROOT_INO ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ str0 ∈ entries3, # links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str)).meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]])) .meta:= md1 ]) ≤ 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 126:
(ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]])).meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) ) = mkdir(m15, md7, m16, m17, entries4), (m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str);mkdir(m8, md5, # links(m0, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries0), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), files[ino] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), dirs0[m0] = mkdir(m8, md5, # links(m0, dirs0), m10, entries3), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries2, entries2[str] ∈ dirs0, m0 ∈ dirs0, ROOT_INO ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str)).meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]])) .meta:= md1 ]) = 1, # links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str)).meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]])) .meta:= md1 ]) = 0, links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str)).meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]])) .meta:= md1 ]) = ∅, str0 ∈ entries3

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)