Nuprl Lemma : eu-midpoint-trivial
∀e:EuclideanPlane. ∀a,b:Point. (a=b=a ⇒ (a = b ∈ Point))
Proof
Definitions occuring in Statement :
eu-midpoint: a=m=b,
euclidean-plane: EuclideanPlane,
eu-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
eu-midpoint: a=m=b,
uimplies: b supposing a,
and: P ∧ Q
Lemmas referenced :
eu-midpoint_wf,
eu-point_wf,
euclidean-plane_wf,
eu-between-eq-same
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
independent_isectElimination,
productElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b:Point. (a=b=a {}\mRightarrow{} (a = b))
Date html generated:
2016_05_18-AM-06_42_24
Last ObjectModification:
2015_12_28-AM-09_22_28
Theory : euclidean!geometry
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