Nuprl Lemma : church-null_wf
∀[A,T:Type]. (church-null() ∈ ((Top ⟶ Top ⟶ Top ⟶ T ⟶ T) ⟶ A) ⟶ A)
Proof
Definitions occuring in Statement :
church-null: church-null(),
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
church-null: church-null()
Lemmas referenced :
church-false_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,T:Type]. (church-null() \mmember{} ((Top {}\mrightarrow{} Top {}\mrightarrow{} Top {}\mrightarrow{} T {}\mrightarrow{} T) {}\mrightarrow{} A) {}\mrightarrow{} A)
Date html generated:
2016_05_15-PM-03_22_34
Last ObjectModification:
2015_12_27-PM-01_05_01
Theory : general
Home
Index