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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