Nuprl Lemma : eu-between-implies-between-eq
∀e:EuclideanPlane. ∀[a,b,c:Point]. a_b_c supposing a-b-c
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-between: a-b-c,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
eu-between-eq-def,
and_wf,
not_wf,
equal_wf,
eu-point_wf,
eu-between_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isectElimination,
hypothesis,
productElimination,
independent_functionElimination,
voidElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c:Point]. a\_b\_c supposing a-b-c
Date html generated:
2016_05_18-AM-06_33_54
Last ObjectModification:
2015_12_28-AM-09_27_50
Theory : euclidean!geometry
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