Nuprl Lemma : eu-between-eq-same
∀[e:EuclideanPlane]. ∀[a,b:Point]. a = b ∈ Point supposing a_b_a
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
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,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
cand: A c∧ B,
false: False
Lemmas referenced :
eu-between-eq_wf,
eu-point_wf,
euclidean-plane_wf,
eu-between-eq-def,
euclidean-point-eq,
not_wf,
equal_wf,
eu-between-same
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_isectElimination,
lambdaFormation,
independent_pairFormation,
voidElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b:Point]. a = b supposing a\_b\_a
Date html generated:
2016_05_18-AM-06_34_22
Last ObjectModification:
2015_12_28-AM-09_27_40
Theory : euclidean!geometry
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