Nuprl Lemma : eu-inner-three-segment
∀e:EuclideanPlane. ∀[a,b,c,A,B,C:Point]. (ab=AB) supposing (bc=BC and ac=AC and A_B_C and a_b_c)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-congruent: ab=cd,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
eu-congruent-trivial,
eu-congruent-iff-length,
eu-length-flip,
eu-inner-five-segment,
eu-congruent_wf,
eu-between-eq_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
hypothesisEquality,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
isect_memberFormation,
setElimination,
rename
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,A,B,C:Point]. (ab=AB) supposing (bc=BC and ac=AC and A\_B\_C and a\_b\_c)
Date html generated:
2016_05_18-AM-06_38_51
Last ObjectModification:
2015_12_28-AM-09_24_01
Theory : euclidean!geometry
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