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Proof step 107 from proof inv-rmdir (previous step)

dirs0[entries0[str]] = mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m2, entries0), dirs = dirs0[m, mkdir(m3, md3, # links(m, dirs0), m2 - 1, entries0 -- str)], ino = entries0[str], afs-cons(dirs0, files), entries0[str] ∈ dirs0, str ∈ entries0, m ∈ dirs0, 1 ≤ m2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, m2 = 0, dirs[ino].nlink ≥ 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 108:
(entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink = 0, dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m2 ⊦ # links(m, dirs0) = 0, entries0[str] = ROOT_INO, links(m, dirs0) = ∅, m = ROOT_INO, m2 = 0

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)