Nuprl Lemma : rel-restriction_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[P:T ⟶ ℙ].  (R|P ∈ T ⟶ T ⟶ ℙ)
Proof
Definitions occuring in Statement : 
rel-restriction: R|P
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
rel-restriction: R|P
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
prop: ℙ
Lemmas referenced : 
and_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lambdaEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
applyEquality, 
hypothesisEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
cumulativity, 
universeEquality, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}].    (R|P  \mmember{}  T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{})
Date html generated:
2016_05_14-AM-06_06_02
Last ObjectModification:
2015_12_26-AM-11_32_39
Theory : relations
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