Nuprl Lemma : sq_stable__geo-gt
∀[g:GeometryPrimitives]. ∀[c,d,a,b:Point]. SqStable(cd > ab)
Proof
Definitions occuring in Statement :
geo-gt: cd > ab,
geo-primitives: GeometryPrimitives,
geo-point: Point,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
sq_stable: SqStable(P),
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo-gt: cd > ab
Lemmas referenced :
geo-primitives_wf,
squash_wf,
geo-sep_wf,
geo-congruent_wf,
geo-between_wf,
geo-point_wf,
exists_wf,
sq_stable__squash
Rules used in proof :
because_Cache,
isect_memberEquality,
baseClosed,
imageMemberEquality,
imageElimination,
dependent_functionElimination,
productEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[g:GeometryPrimitives]. \mforall{}[c,d,a,b:Point]. SqStable(cd > ab)
Date html generated:
2017_10_02-PM-03_25_58
Last ObjectModification:
2017_08_04-PM-05_50_51
Theory : euclidean!plane!geometry
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