Nuprl Lemma : isect-rel_wf
∀[T,A:Type]. ∀[R:T ⟶ A ⟶ A ⟶ ℙ]. (isect-rel(T;i.R[i]) ∈ A ⟶ A ⟶ ℙ)
Proof
Definitions occuring in Statement :
isect-rel: isect-rel(T;i.R[i]),
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,
isect-rel: isect-rel(T;i.R[i]),
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T,A:Type]. \mforall{}[R:T {}\mrightarrow{} A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (isect-rel(T;i.R[i]) \mmember{} A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_04_52
Last ObjectModification:
2015_12_26-AM-11_32_58
Theory : relations
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