Nuprl Lemma : eu-three-segment
∀e:EuclideanPlane. ∀[a,b,c,A,B,C:Point]. (ac=AC) 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 :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
euclidean-plane: EuclideanPlane,
prop: ℙ
Lemmas referenced :
eu-five-segment,
eu-point_wf,
eu-congruent_wf,
eu-between-eq_wf,
not_wf,
equal_wf,
euclidean-plane_wf,
eu-congruent-trivial,
eu-congruent-comm
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberFormation,
isectElimination,
introduction,
sqequalRule,
lambdaEquality,
voidElimination,
equalityEquality,
setElimination,
rename,
independent_isectElimination,
because_Cache
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,A,B,C:Point]. (ac=AC) 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_20
Last ObjectModification:
2015_12_28-AM-09_26_22
Theory : euclidean!geometry
Home
Index