Nuprl Lemma : least-equiv_wf
∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ]. (least-equiv(A;R) ∈ A ⟶ A ⟶ ℙ)
Proof
Definitions occuring in Statement :
least-equiv: least-equiv(A;R),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
least-equiv: least-equiv(A;R),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
or_wf,
transitive-reflexive-closure_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
universeEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
functionExtensionality,
applyEquality,
lambdaEquality,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (least-equiv(A;R) \mmember{} A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{})
Date html generated:
2018_05_21-PM-00_51_46
Last ObjectModification:
2018_01_08-AM-01_05_41
Theory : relations2
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