Nuprl Lemma : transitive-reflexive-closure_wf
∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ]. (R^* ∈ A ⟶ A ⟶ ℙ)
Proof
Definitions occuring in Statement :
transitive-reflexive-closure: R^*,
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,
transitive-reflexive-closure: R^*,
prop: ℙ
Lemmas referenced :
or_wf,
equal_wf,
transitive-closure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (R\^{}* \mmember{} A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{})
Date html generated:
2017_01_19-PM-02_17_38
Last ObjectModification:
2017_01_14-PM-04_22_25
Theory : relations2
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