Nuprl Lemma : eu-congruent-comm
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. ba=dc supposing 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,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
euclidean-plane_wf,
eu-point_wf,
eu-congruent_wf,
eu-congruent-right-comm,
eu-congruent-left-comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
independent_isectElimination,
hypothesis,
because_Cache,
setElimination,
rename
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. ba=dc supposing ab=cd
Date html generated:
2016_05_18-AM-06_35_04
Last ObjectModification:
2016_04_28-PM-06_40_35
Theory : euclidean!geometry
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