Nuprl Lemma : church-ite_wf
∀[A,B,C:Type]. (church-ite() ∈ (A ⟶ B ⟶ C) ⟶ A ⟶ B ⟶ C)
Proof
Definitions occuring in Statement :
church-ite: church-ite(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
church-ite: church-ite()
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
functionEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache
Latex:
\mforall{}[A,B,C:Type]. (church-ite() \mmember{} (A {}\mrightarrow{} B {}\mrightarrow{} C) {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} C)
Date html generated:
2016_05_15-PM-03_22_11
Last ObjectModification:
2015_12_27-PM-01_04_45
Theory : general
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