Nuprl Lemma : eta_conv
∀[A,B:Type]. ∀[f:A ⟶ B]. ((λx.(f x)) = f ∈ (A ⟶ B))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
applyEquality,
hypothesisEquality,
hypothesis,
functionEquality,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. ((\mlambda{}x.(f x)) = f)
Date html generated:
2016_05_13-PM-04_04_32
Last ObjectModification:
2015_12_26-AM-11_05_19
Theory : fun_1
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