### Nuprl Lemma : eu-fsc-ap

`∀e:EuclideanPlane. ∀a,b,c,d,a',b',c',d':Point.  (FSC(a;b;c;d  a';b';c';d') `` (¬(a = b ∈ Point)) `` cd=c'd')`

Proof

Definitions occuring in Statement :  eu-five-seg-compressed: `FSC(a;b;c;d  a';b';c';d')` euclidean-plane: `EuclideanPlane` eu-congruent: `ab=cd` eu-point: `Point` all: `∀x:A. B[x]` not: `¬A` implies: `P `` Q` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` euclidean-plane: `EuclideanPlane` eu-five-seg-compressed: `FSC(a;b;c;d  a';b';c';d')` uimplies: `b supposing a` and: `P ∧ Q` eu-cong-tri: `Cong3(abc,a'b'c')` uiff: `uiff(P;Q)`
Lemmas referenced :  not_wf equal_wf eu-point_wf eu-five-seg-compressed_wf euclidean-plane_wf eu-colinear-five-segment eu-congruent-iff-length eu-length-flip
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis dependent_functionElimination independent_isectElimination productElimination because_Cache equalityTransitivity equalitySymmetry

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c,d,a',b',c',d':Point.    (FSC(a;b;c;d    a';b';c';d')  {}\mRightarrow{}  (\mneg{}(a  =  b))  {}\mRightarrow{}  cd=c'd')

Date html generated: 2016_05_18-AM-06_42_14
Last ObjectModification: 2015_12_28-AM-09_22_42

Theory : euclidean!geometry

Home Index