Nuprl Lemma : eu-congruent-symmetry
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. cd=ab 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,
sq_stable: SqStable(P),
implies: P ⇒ Q,
euclidean-axioms: euclidean-axioms(e),
and: P ∧ Q,
squash: ↓T
Lemmas referenced :
eu-congruent-refl,
sq_stable__eu-congruent,
euclidean-plane_wf,
eu-point_wf,
eu-congruent_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
introduction,
productElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. cd=ab supposing ab=cd
Date html generated:
2016_05_18-AM-06_34_48
Last ObjectModification:
2016_01_16-PM-10_30_59
Theory : euclidean!geometry
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