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Proof step 35 from proof abs-nlinks-h (previous step)

tree[p0] = dnode(md, sdt), tree[p0 + str '] = fnode(⌜ino1⌝ ), links(ino1, dirs) = ∅, ((m0 => mkdir(# entries, md, m1, m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p0, m0)) )(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ sdt, p0 ∈ tree, ino1 ∈ files, ino0 ∈ dirs, str ∈ entries, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 37:
tree[p0 + str '] = fnode(⌜ino1⌝ ), tree[p0] = dnode(md, sdt), ((m0 => mkdir(# entries, md, m1, m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p0, m0)) )(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ entries, ino0 ∈ dirs, ino1 ∈ files, p0 ∈ tree, str ∈ sdt, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ alink. alink ∈ links(ino1, dirs) ↔ alink ∈ ∅, entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [∅, links(ino1, dirs)] flags: <all paths>

Additional information

Used terms: ∅, links(ino1, dirs)