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