Nuprl Lemma : sq_stable__meq
∀[X:Type]. ∀[d:metric(X)]. ∀[x,y:X]. SqStable(x ≡ y)
Proof
Definitions occuring in Statement :
meq: x ≡ y,
metric: metric(X),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
meq: x ≡ y,
metric: metric(X),
sq_stable: SqStable(P),
implies: P ⇒ Q
Lemmas referenced :
sq_stable__req,
int-to-real_wf,
req_witness,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
independent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[x,y:X]. SqStable(x \mequiv{} y)
Date html generated:
2019_10_29-AM-10_54_34
Last ObjectModification:
2019_10_02-AM-09_36_03
Theory : reals
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