Nuprl Lemma : geo-out2-bet-out
∀e:BasicGeometry. ∀a,b,c,x,p:Point. (out(b ac) ⇒ out(b xp) ⇒ a_x_c ⇒ {out(b ap) ∧ out(b cp)})
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-between: a_b_c,
geo-point: Point,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
uimplies: b supposing a,
false: False,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
not: ¬A,
guard: {T},
and: P ∧ Q,
geo-out: out(p ab),
implies: P ⇒ Q,
all: ∀x:A. B[x],
cand: A c∧ B
Lemmas referenced :
geo-point_wf,
geo-out_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
not_wf,
geo-between_wf,
geo-between-exchange4,
geo-between-exchange3,
geo-between-inner-trans,
geo-between-symmetry,
geo-between-same-side,
geo-between-middle
Rules used in proof :
independent_isectElimination,
instantiate,
productEquality,
voidElimination,
sqequalRule,
because_Cache,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
independent_functionElimination,
hypothesis,
independent_pairFormation,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,x,p:Point. (out(b ac) {}\mRightarrow{} out(b xp) {}\mRightarrow{} a\_x\_c {}\mRightarrow{} \{out(b ap) \mwedge{} out(b cp)\})
Date html generated:
2017_10_02-PM-06_27_28
Last ObjectModification:
2017_08_05-PM-04_20_46
Theory : euclidean!plane!geometry
Home
Index