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Proof step 29 from proof plinks-fids (previous step)

# links(fid1, dnode(md, sdt0)) = count(fid1, sdt0.fids), ∀ str0. str0 ∈ sdt0[str, tree] → (∀ fid1. # links(fid1, sdt0[str, tree][str0]) = count(fid1, sdt0[str, tree][str0].fids)), ∀ sdt1, fid1, md. # sdt1 < # sdt0[str, tree] → (∀ str. str ∈ sdt1 → (∀ fid1. # links(fid1, sdt1[str]) = count(fid1, sdt1[str].fids))) → # links(fid1, dnode(md, sdt1)) = count(fid1, sdt1.fids) ⊦ #(links(fid1, dnode(md, sdt0)) ∪ (str + links(fid1, tree))) = count(fid1, sdt0.fids) + # links(fid1, tree), links(fid1, dnode(md, sdt0)) ∩ (str + links(fid1, tree)) = ∅, str ∈ sdt0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# links(fid1, dnode(md, sdt0)) = count(fid1, sdt0.fids), ∀ str0. str0 ∈ sdt0[str, tree] → (∀ fid1. # links(fid1, sdt0[str, tree][str0]) = count(fid1, sdt0[str, tree][str0].fids)), ∀ sdt1, fid1, md. # sdt1 < # sdt0[str, tree] → (∀ str. str ∈ sdt1 → (∀ fid1. # links(fid1, sdt1[str]) = count(fid1, sdt1[str].fids))) → # links(fid1, dnode(md, sdt1)) = count(fid1, sdt1.fids) ⊦ #(links(fid1, dnode(md, sdt0)) ∩ (str + links(fid1, tree))) = 0, #(links(fid1, dnode(md, sdt0)) ∪ (str + links(fid1, tree))) = count(fid1, sdt0.fids) + # links(fid1, tree), links(fid1, dnode(md, sdt0)) ∩ (str + links(fid1, tree)) = ∅, str ∈ sdt0

Rule argument

Additional information

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