Nuprl Lemma : stable__geo-congruent
∀g:EuclideanPlaneStructure. ∀[a,b,c,d:Point]. Stable{ab ≅ cd}
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
geo-congruent: ab ≅ cd,
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
false: False,
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
stable: Stable{P},
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo-congruent: ab ≅ cd,
all: ∀x:A. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
geo-length-sep_wf,
stable__not
Rules used in proof :
universeIsType,
voidElimination,
isectIsTypeImplies,
inhabitedIsType,
functionIsTypeImplies,
because_Cache,
dependent_functionElimination,
lambdaEquality_alt,
isect_memberEquality_alt,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalRule,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlaneStructure. \mforall{}[a,b,c,d:Point]. Stable\{ab \mcong{} cd\}
Date html generated:
2019_10_29-AM-09_13_14
Last ObjectModification:
2019_10_28-AM-09_51_44
Theory : euclidean!plane!geometry
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