Nuprl Lemma : eu-congruent-flip-seg
∀e:EuclideanPlane. ∀[a,b:Point]. ab ≡ ba
Proof
Definitions occuring in Statement :
eu-seg-congruent: s1 ≡ s2,
eu-mk-seg: ab,
euclidean-plane: EuclideanPlane,
eu-point: Point,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
eu-seg-congruent: s1 ≡ s2,
member: t ∈ T,
top: Top,
euclidean-plane: EuclideanPlane
Lemmas referenced :
eu_seg1_mk_seg_lemma,
eu_seg2_mk_seg_lemma,
eu-congruent-flip,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
isectElimination,
setElimination,
rename
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b:Point]. ab \mequiv{} ba
Date html generated:
2016_05_18-AM-06_37_12
Last ObjectModification:
2015_12_28-AM-09_25_14
Theory : euclidean!geometry
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