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Proof step 30 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))) = 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ ps = ps0 ↔ (∀ p. p ∈ ps ↔ p ∈ ps0)
Proof step 32:
# 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))) = 0, str ∈ sdt0, ∀ p. p ∈ links(fid1, dnode(md, sdt0)) ∩ (str + links(fid1, tree)) ↔ p ∈ ∅

Rule argument

spec: set-basic, inst: pathset name: Extension seq: ⊦ ps = ps0 ↔ (∀ p. p ∈ ps ↔ p ∈ ps0) subst: [ps0, ps] → [∅, links(fid1, dnode(md, sdt0)) ∩ (str + links(fid1, tree))] flags: <all paths>

Additional information

Used terms: ∅, links(fid1, dnode(md, sdt0)) ∩ (str + links(fid1, tree))