Nuprl Lemma : eu-inner-five-segment'
∀e:EuclideanPlane
∀[a,b,c,A,B,C:Point]. (∀d,D:Point. (bd=BD) supposing (cd=CD and ad=AD)) supposing (bc=BC and ac=AC and A_B_C and a_b\000C_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 :
euclidean-plane: EuclideanPlane,
prop: ℙ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
eu-inner-five-segment,
eu-congruent_wf,
eu-point_wf,
eu-between-eq_wf,
euclidean-plane_wf
Rules used in proof :
rename,
setElimination,
independent_isectElimination,
isectElimination,
isect_memberFormation,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
lemma_by_obid,
cut
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,A,B,C:Point].
(\mforall{}d,D:Point. (bd=BD) supposing (cd=CD and ad=AD)) supposing (bc=BC and ac=AC and A\_B\_C and a\_b\_\000Cc)
Date html generated:
2016_05_18-AM-06_38_48
Last ObjectModification:
2016_01_02-PM-00_14_01
Theory : euclidean!geometry
Home
Index