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Proof step 76 from proof crash-neutral-rmdir (previous step)

dirs0[m] = mkdir(m1 + 1, md3, # links(m, dirs0), m4, entries0), dirs0[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅), dirs = dirs0[m, mkdir(m1, md3, # links(m, dirs0), m4 - 1, entries0 -- str)], files0 = files, ino = entries0[str], afs-cons(dirs0, files), str ∈ entries0, entries0[str] ∈ dirs0, m ∈ dirs0, 1 ≤ m4, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, entries0[str] = ROOT_INO, m4 = 0, dirs[ino].nlink ≥ 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
(entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m4 - 1, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) .nlink = 0, dirs0[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅), dirs0[m] = mkdir(m1 + 1, md3, # links(m, dirs0), m4, entries0), # links(m, dirs0) ≠ 0, entries0[str] ≠ ROOT_INO, links(m, dirs0) ≠ ∅, m ≠ ROOT_INO, m4 ≠ 0, afs-cons(dirs0, files), m ∈ dirs0, entries0[str] ∈ dirs0, str ∈ entries0, 1 ≤ m4 ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced

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)