Nuprl Lemma : geo-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_c)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-between: a_b_c,
geo-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],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
geo-inner-five-segment,
geo-congruent_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf,
geo-between_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberFormation,
isectElimination,
independent_isectElimination,
applyEquality,
instantiate,
sqequalRule,
because_Cache
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,A,B,C:Point].
(\mforall{}d,D:Point. (bd \00D0 BD) supposing (cd \00D0 CD and ad \00D0 AD)) supposing
(bc \00D0 BC and
ac \00D0 AC and
A\_B\_C and
a\_b\_c)
Date html generated:
2017_10_02-PM-04_41_41
Last ObjectModification:
2017_08_10-PM-01_14_01
Theory : euclidean!plane!geometry
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