Nuprl Lemma : eu-congruence-identity2
∀[e:EuclideanPlane]. ∀[a,b,c,d:Point]. (a = b ∈ Point) supposing (ab=cd and (c = d ∈ Point))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-congruent: ab=cd,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
eu-congruent_wf,
eu-congruence-identity,
equal_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
equalitySymmetry,
thin,
hyp_replacement,
Error :applyLambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesisEquality,
sqequalRule,
independent_isectElimination,
isect_memberEquality,
axiomEquality,
equalityTransitivity
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b,c,d:Point]. (a = b) supposing (ab=cd and (c = d))
Date html generated:
2016_10_26-AM-07_40_48
Last ObjectModification:
2016_07_12-AM-08_06_46
Theory : euclidean!geometry
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