Nuprl Lemma : geo-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 ≠ \000Cb)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-between: a_b_c,
geo-sep: a ≠ b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-sep_wf,
geo-between_wf,
geo-point_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-congruent_wf,
geo-five-segment
Rules used in proof :
because_Cache,
sqequalRule,
instantiate,
applyEquality,
hypothesis,
independent_isectElimination,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
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 \00D0 CD) supposing (bd \00D0 BD and ad \00D0 AD)) supposing
(bc \00D0 BC and
ab \00D0 AB and
A\_B\_C and
a\_b\_c and
a \mneq{} b)
Date html generated:
2017_10_02-PM-03_28_54
Last ObjectModification:
2017_08_04-PM-09_32_41
Theory : euclidean!plane!geometry
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