Nuprl Lemma : sq_stable__geo-congruent
∀g:EuclideanPlaneStructure. ∀[a,b,c,d:Point]. SqStable(ab ≅ cd)
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
geo-congruent: ab ≅ cd,
geo-point: Point,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
stable__geo-congruent,
geo-congruent_wf,
stable-implies-sq_stable
Rules used in proof :
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlaneStructure. \mforall{}[a,b,c,d:Point]. SqStable(ab \00D0 cd)
Date html generated:
2017_10_02-PM-03_26_31
Last ObjectModification:
2017_08_05-PM-03_34_55
Theory : euclidean!plane!geometry
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