Nuprl Lemma : cond_rel_implies_wf
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀[R1,R2:T ⟶ T ⟶ ℙ].  (when P, R1 => R2 ∈ ℙ)
Proof
Definitions occuring in Statement : 
cond_rel_implies: when P, R1 => R2
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
cond_rel_implies: when P, R1 => R2
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
infix_ap: x f y
, 
so_apply: x[s]
Lemmas referenced : 
all_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
functionEquality, 
applyEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
Error :inhabitedIsType, 
isect_memberEquality, 
cumulativity, 
universeEquality, 
Error :functionIsType, 
Error :universeIsType, 
because_Cache
Latex:
\mforall{}[T:Type].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[R1,R2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (when  P,  R1  =>  R2  \mmember{}  \mBbbP{})
Date html generated:
2019_06_20-PM-00_30_30
Last ObjectModification:
2018_09_26-PM-00_39_28
Theory : relations
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