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Proof step 6 from proof afs-cons-links-rmorphans (previous step)

afs-cons(dirs, files), alink.name ∈ dirs[alink.pino].entries, alink.pino ∈ dirs, alink.pino ∈ orphans(dirs, files) ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
alink = mklink(m, str), afs-cons(dirs, files), m ∈ orphans(dirs, files), m ∈ dirs, str ∈ dirs[m].entries ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅

Rule argument

spec: alink name: elim seq: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str) subst: [alink, m, str] → [alink, m, str]

Additional information

Used simplifier rules: ⊦ m = alink.pino ∧ str = alink.name ↔ alink = mklink(m, str); (elim) Used terms: alink, m, str