Nuprl Lemma : predicate_implies_wf
∀[T:Type]. ∀[P1,P2:T ⟶ ℙ].  (P1 
⇒ P2 ∈ ℙ)
Proof
Definitions occuring in Statement : 
predicate_implies: P1 
⇒ P2
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
predicate_implies: P1 
⇒ P2
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
so_apply: x[s]
Lemmas referenced : 
all_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
functionEquality, 
applyEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
cumulativity, 
universeEquality, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[T:Type].  \mforall{}[P1,P2:T  {}\mrightarrow{}  \mBbbP{}].    (P1  {}\mRightarrow{}  P2  \mmember{}  \mBbbP{})
Date html generated:
2016_05_14-AM-06_05_36
Last ObjectModification:
2015_12_26-AM-11_32_40
Theory : relations
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