Nuprl Lemma : implies-least-equiv
∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ]. R => least-equiv(A;R)
Proof
Definitions occuring in Statement :
least-equiv: least-equiv(A;R),
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
infix_ap: x f y,
prop: ℙ,
member: t ∈ T,
least-equiv: least-equiv(A;R),
implies: P ⇒ Q,
all: ∀x:A. B[x],
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
or: P ∨ Q
Lemmas referenced :
or_wf,
transitive-reflexive-closure-base-case
Rules used in proof :
universeEquality,
functionEquality,
independent_functionElimination,
dependent_functionElimination,
hypothesis,
cumulativity,
hypothesisEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
because_Cache,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
inlFormation,
sqequalRule
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. R => least-equiv(A;R)
Date html generated:
2018_05_21-PM-00_51_57
Last ObjectModification:
2018_01_08-AM-10_15_33
Theory : relations2
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