Nuprl Lemma : geo-strict-between-trans
∀e:BasicGeometry-. ∀a,b,c,d:Point. (a-b-d ⇒ b-c-d ⇒ a-b-c)
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-strict-between: a-b-c,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
basic-geo-axioms: BasicGeometryAxioms(g),
cand: A c∧ B,
and: P ∧ Q,
geo-strict-between: a-b-c,
sq_stable: SqStable(P),
member: t ∈ T,
basic-geometry-: BasicGeometry-,
implies: P ⇒ Q,
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-strict-between
Rules used in proof :
because_Cache,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
imageElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
independent_pairFormation,
productElimination,
independent_functionElimination,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
rename,
thin,
setElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry-. \mforall{}a,b,c,d:Point. (a-b-d {}\mRightarrow{} b-c-d {}\mRightarrow{} a-b-c)
Date html generated:
2017_10_02-PM-04_42_11
Last ObjectModification:
2017_08_05-AM-08_41_28
Theory : euclidean!plane!geometry
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