Nuprl Lemma : geo-strict-between-sym
∀e:BasicGeometry-. ∀a,b,c:Point. (a-b-c ⇒ c-b-a)
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 :
all: ∀x:A. B[x],
implies: P ⇒ Q,
basic-geometry-: BasicGeometry-,
euclidean-plane: EuclideanPlane,
member: t ∈ T,
sq_stable: SqStable(P),
geo-strict-between: a-b-c,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
squash: ↓T,
guard: {T}
Lemmas referenced :
sq_stable__geo-strict-between,
geo-between-symmetry,
basic-geo-axioms_wf,
euclidean-plane-structure-subtype,
geo-left-axioms_wf,
geo-sep-sym,
geo-strict-between_wf,
euclidean-plane-subtype,
basic-geometry--subtype,
subtype_rel_transitivity,
basic-geometry-_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
productElimination,
independent_pairFormation,
dependent_set_memberEquality,
productEquality,
isectElimination,
applyEquality,
sqequalRule,
because_Cache,
independent_isectElimination,
imageMemberEquality,
baseClosed,
imageElimination,
instantiate
Latex:
\mforall{}e:BasicGeometry-. \mforall{}a,b,c:Point. (a-b-c {}\mRightarrow{} c-b-a)
Date html generated:
2017_10_02-PM-04_42_08
Last ObjectModification:
2017_09_29-AM-11_39_01
Theory : euclidean!plane!geometry
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