Nuprl Lemma : eu-five-segment'
∀e:EuclideanPlane
∀[a,b,c,A,B,C:Point].
(∀d,D:Point. (cd=CD) supposing (bd=BD and ad=AD)) supposing
(bc=BC and
ab=AB and
A_B_C and
a_b_c and
(¬(a = b ∈ Point)))
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],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
prop: ℙ,
euclidean-plane: EuclideanPlane,
false: False,
implies: P ⇒ Q,
not: ¬A,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
eu-point_wf,
eu-five-segment,
eu-congruent_wf,
eu-between-eq_wf,
not_wf,
equal_wf,
euclidean-plane_wf
Rules used in proof :
independent_isectElimination,
hypothesis,
rename,
setElimination,
isectElimination,
lemma_by_obid,
equalityEquality,
voidElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,A,B,C:Point].
(\mforall{}d,D:Point. (cd=CD) supposing (bd=BD and ad=AD)) supposing
(bc=BC and
ab=AB and
A\_B\_C and
a\_b\_c and
(\mneg{}(a = b)))
Date html generated:
2016_05_18-AM-06_35_17
Last ObjectModification:
2016_01_02-PM-00_16_04
Theory : euclidean!geometry
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