Nuprl Lemma : stable_point-eq
∀[e:EuclideanPlane]. ∀[p,q:Point]. Stable{p = q ∈ Point}
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
stable: Stable{P},
uimplies: b supposing a,
prop: ℙ,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
guard: {T},
sq_stable: SqStable(P),
squash: ↓T,
euclidean-axioms: euclidean-axioms(e),
and: P ∧ Q
Lemmas referenced :
not_wf,
equal_wf,
eu-point_wf,
euclidean-plane_wf,
stable__eu-congruent,
eu-congruent_wf,
sq_stable__eu-congruent,
eu-congruence-identity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
voidElimination,
hyp_replacement,
Error :applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[p,q:Point]. Stable\{p = q\}
Date html generated:
2016_10_26-AM-07_40_52
Last ObjectModification:
2016_07_12-AM-08_06_51
Theory : euclidean!geometry
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