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Proof step 7 from proof afs-cons-nlink0-notin (previous step)

alink = mklink(m, str), afs-cons(dirs, files), str ∈ dirs[m].entries, m ∈ dirs ⊦ # links(dirs[m].entries[str], dirs) = 0, links(dirs[m].entries[str], dirs) = ∅, dirs[m].entries[str] ∈ dirs, dirs[m].entries[str] ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m].entries ⊦ # links(dirs[m].entries[str], dirs) = 0, links(dirs[m].entries[str], dirs) = ∅, dirs[m].entries[str] ∈ files, dirs[m].entries[str] ∈ dirs

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]