Nuprl Lemma : sq_stable__circle-overlap
∀[g:GeometryPrimitives]. ∀[a,b,c,d:Point]. SqStable(Overlap(a;b;c;d))
Proof
Definitions occuring in Statement :
circle-overlap: Overlap(a;b;c;d),
geo-primitives: GeometryPrimitives,
geo-point: Point,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
circle-overlap: Overlap(a;b;c;d),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
sq_stable__squash,
exists_wf,
geo-point_wf,
geo-congruent_wf,
geo-ge_wf,
squash_wf,
circle-overlap_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
because_Cache,
productEquality,
dependent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality
Latex:
\mforall{}[g:GeometryPrimitives]. \mforall{}[a,b,c,d:Point]. SqStable(Overlap(a;b;c;d))
Date html generated:
2017_10_02-PM-03_26_15
Last ObjectModification:
2017_08_12-PM-06_19_09
Theory : euclidean!plane!geometry
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