Nuprl Lemma : eu-congruence-identity
∀[e:EuclideanPlane]. ∀[a,b,c:Point]. a = b ∈ Point supposing ab=cc
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,
euclidean-plane: EuclideanPlane,
prop: ℙ,
guard: {T},
euclidean-axioms: euclidean-axioms(e),
and: P ∧ Q
Lemmas referenced :
eu-congruent_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b,c:Point]. a = b supposing ab=cc
Date html generated:
2016_05_18-AM-06_33_59
Last ObjectModification:
2015_12_28-AM-09_27_42
Theory : euclidean!geometry
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