Nuprl Lemma : rel_inverse_wf
∀[T1,T2:Type]. ∀[R:T1 ⟶ T2 ⟶ ℙ].  (R^-1 ∈ T2 ⟶ T1 ⟶ ℙ)
Proof
Definitions occuring in Statement : 
rel_inverse: R^-1
, 
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
, 
rel_inverse: R^-1
, 
infix_ap: x f y
, 
prop: ℙ
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
lambdaEquality, 
applyEquality, 
hypothesisEquality, 
sqequalHypSubstitution, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
Error :functionIsType, 
Error :universeIsType, 
universeEquality, 
isect_memberEquality, 
isectElimination, 
thin, 
functionEquality, 
cumulativity, 
Error :inhabitedIsType, 
because_Cache
Latex:
\mforall{}[T1,T2:Type].  \mforall{}[R:T1  {}\mrightarrow{}  T2  {}\mrightarrow{}  \mBbbP{}].    (R\^{}-1  \mmember{}  T2  {}\mrightarrow{}  T1  {}\mrightarrow{}  \mBbbP{})
Date html generated:
2019_06_20-PM-00_30_53
Last ObjectModification:
2018_09_26-PM-00_39_30
Theory : relations
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