Nuprl Lemma : predicate_implies_reflexivity
∀[T:Type]. ∀[P:T ⟶ ℙ].  P 
⇒ P
Proof
Definitions occuring in Statement : 
predicate_implies: P1 
⇒ P2
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
predicate_implies: P1 
⇒ P2
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
prop: ℙ
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
lambdaFormation, 
hypothesis, 
applyEquality, 
hypothesisEquality, 
functionEquality, 
cumulativity, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}].    P  {}\mRightarrow{}  P
Date html generated:
2016_05_14-AM-06_05_51
Last ObjectModification:
2015_12_26-AM-11_32_19
Theory : relations
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