Nuprl Lemma : ccomb_wf
∀[P,A,B:Type]. (C ∈ (A ⟶ B ⟶ P) ⟶ B ⟶ A ⟶ P)
Proof
Definitions occuring in Statement :
ccomb: C,
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,
ccomb: C
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{}[P,A,B:Type]. (C \mmember{} (A {}\mrightarrow{} B {}\mrightarrow{} P) {}\mrightarrow{} B {}\mrightarrow{} A {}\mrightarrow{} P)
Date html generated:
2016_05_13-PM-03_53_14
Last ObjectModification:
2015_12_26-AM-10_16_52
Theory : bar-induction
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