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Proof step 40 from proof abs-nlinks-h (previous step)

tree[p0] = dnode(md, sdt), tree[p0 + str '] = fnode(⌜ino1⌝ ), ((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, ∀ alink. ¬ alink.pino ∈ dirs ∨ ¬ alink.name ∈ dirs[alink.pino].entries ∨ ino1 ≠ dirs[alink.pino].entries[alink.name], entries[str] ∈ dirs ∨ entries[str] ∈ files, ¬ str ∈ dirs[m0].entries ∨ ino1 ≠ dirs[m0].entries[str] ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 41:
tree[p0 + str '] = fnode(⌜ino1⌝ ), tree[p0] = dnode(md, sdt), dirs[m0] = mkdir(m, md0, m3, m4, entries0), ((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, ∀ alink. ¬ alink.pino ∈ dirs ∨ ¬ alink.name ∈ dirs[alink.pino].entries ∨ ino1 ≠ dirs[alink.pino].entries[alink.name], ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ¬ str ∈ entries0 ∨ ino1 ≠ entries0[str], entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, entries] → [dirs[m0], m2, md0, m3, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m0], m2, md0, m3, entries