Nuprl Lemma : bigrel_wf
∀[T:𝕌']. ∀[F:(T ⟶ T ⟶ ℙ) ⟶ T ⟶ T ⟶ ℙ]. (νR.F[R] ∈ T ⟶ T ⟶ ℙ)
Proof
Definitions occuring in Statement :
bigrel: νR.F[R],
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bigrel: νR.F[R],
isect-rel: ⋂i:T. R[i],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
nat: ℕ
Lemmas referenced :
all_wf,
nat_wf,
primrec_wf,
true_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
instantiate,
functionEquality,
hypothesisEquality,
universeEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:\mBbbU{}']. \mforall{}[F:(T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}) {}\mrightarrow{} T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (\mnu{}R.F[R] \mmember{} T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_31_31
Last ObjectModification:
2018_08_04-PM-05_14_24
Theory : relations
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