Nuprl Lemma : eu-seg-length-test
∀e:EuclideanPlane. ∀[a,b,c,d,x,y:Point]. (ba=xy) supposing (dc=yx and ab=cd)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-congruent: ab=cd,
eu-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],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
euclidean-plane_wf,
eu-point_wf,
eu-congruent_wf,
eu-length-flip,
eu-congruent-iff-length
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
productElimination,
independent_isectElimination,
because_Cache,
hypothesis,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d,x,y:Point]. (ba=xy) supposing (dc=yx and ab=cd)
Date html generated:
2016_05_18-AM-06_41_17
Last ObjectModification:
2016_01_04-PM-02_45_44
Theory : euclidean!geometry
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