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Proof step 20 from proof abs-nlinks-h (previous step)

tree[p0 + str '] = fnode(⌜ino1⌝ ), links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ino0 ∈ dirs, str ' ∈ tree[p0], p0 ∈ tree, ino1 ∈ files, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∃ m0. ispath(p0, ino0, m0, dirs, files) ∧ ispath(str ', m0, m, dirs, files) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
tree[p0 + str '] = fnode(⌜ino1⌝ ), links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ dirs[m0].entries, m0 ∈ dirs, ino0 ∈ dirs, str ' ∈ tree[p0], p0 ∈ tree, ino1 ∈ files, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, dirs[m0].entries[str] ∈ dirs ∨ dirs[m0].entries[str] ∈ files ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ispath(str ', n, m, dirs, files) ↔ n ∈ dirs ∧ str ∈ dirs[n].entries ∧ (m ∈ dirs ∨ m ∈ files) ∧ dirs[n].entries[str] = m; (s)