[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

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

∀ fid. fid ∈ fids ↔ fid ∈ tree.fids, ∀ str0. str0 ∈ sdt0[str, tree] → (∃ fids. ∀ fid. fid ∈ fids ↔ fid ∈ sdt0[str, tree][str0].fids), ∀ fid0. fid0 ∈ fids0 ↔ fid0 ∈ sdt0.fids, ∀ sdt1. # sdt1 < # sdt0[str, tree] → (∀ str. str ∈ sdt1 → (∃ fids. ∀ fid. fid ∈ fids ↔ fid ∈ sdt1[str].fids)) → (∃ fids. ∀ fid0. fid0 ∈ fids ↔ fid0 ∈ sdt1.fids) ⊦ fid ∈ fids ∨ fid ∈ fids0 ↔ fid ∈ sdt0.fids ∪ tree.fids, str ∈ sdt0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0
Proof step 31:
∀ fid0. fid0 ∈ fids0 ↔ fid0 ∈ sdt0.fids, ∀ str0. str0 ∈ sdt0[str, tree] → (∃ fids. ∀ fid. fid ∈ fids ↔ fid ∈ sdt0[str, tree][str0].fids), ∀ fid. fid ∈ fids ↔ fid ∈ tree.fids, ∀ sdt1. # sdt1 < # sdt0[str, tree] → (∀ str. str ∈ sdt1 → (∃ fids. ∀ fid. fid ∈ fids ↔ fid ∈ sdt1[str].fids)) → (∃ fids. ∀ fid0. fid0 ∈ fids ↔ fid0 ∈ sdt1.fids) ⊦ fid ∈ fids ∨ fid ∈ fids0 ↔ fid ∈ sdt0.fids ∨ fid ∈ tree.fids, str ∈ sdt0

Rule argument

spec: bag-union, inst: fidbag name: in-union seq: ⊦ fid ∈ fidb ∪ fidb0 ↔ fid ∈ fidb ∨ fid ∈ fidb0 subst: [fidb0, fidb, fid] → [tree.fids, sdt0.fids, fid] flags: <all paths>

Additional information

Used terms: tree.fids, sdt0.fids, fid