Nuprl Lemma : C-comb_wf
∀[A,B,C:Type]. (C-comb() ∈ (A ⟶ B ⟶ C) ⟶ B ⟶ A ⟶ C)
Proof
Definitions occuring in Statement :
C-comb: C-comb(),
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,
C-comb: C-comb()
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]. (C-comb() \mmember{} (A {}\mrightarrow{} B {}\mrightarrow{} C) {}\mrightarrow{} B {}\mrightarrow{} A {}\mrightarrow{} C)
Date html generated:
2016_05_15-PM-05_45_06
Last ObjectModification:
2015_12_27-PM-00_29_21
Theory : general
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