Nuprl Lemma : geo-strict-between-implies-between
∀e:BasicGeometry-. ∀[a,b,c:Point]. a_b_c supposing a-b-c
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-strict-between: a-b-c,
geo-between: a_b_c,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
squash: ↓T,
and: P ∧ Q,
geo-strict-between: a-b-c,
implies: P ⇒ Q,
sq_stable: SqStable(P),
basic-geometry-: BasicGeometry-,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry-_wf,
subtype_rel_transitivity,
basic-geometry--subtype,
geo-strict-between_wf,
sq_stable__geo-between
Rules used in proof :
because_Cache,
independent_isectElimination,
instantiate,
applyEquality,
imageElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
productElimination,
independent_functionElimination,
isectElimination,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry-. \mforall{}[a,b,c:Point]. a\_b\_c supposing a-b-c
Date html generated:
2017_10_02-PM-04_43_23
Last ObjectModification:
2017_08_05-AM-09_07_46
Theory : euclidean!plane!geometry
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