Nuprl Lemma : geo-bet-out-out-bet
∀e:BasicGeometry. ∀b,a,a',c,c':Point. (a_b_c ⇒ out(b aa') ⇒ out(b cc') ⇒ a'_b_c')
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
not: ¬A,
uimplies: b supposing a,
stable: Stable{P},
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
member: t ∈ T,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
geo-out: out(p ab),
false: False
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-sep_wf,
geo-between_wf,
not_wf,
stable__geo-between,
geo-between-exchange3,
geo-between-inner-trans,
geo-between-exchange4,
geo-sep-sym,
geo-between-outer-trans,
geo-between-symmetry
Rules used in proof :
instantiate,
productEquality,
because_Cache,
applyEquality,
independent_isectElimination,
isectElimination,
hypothesis,
hypothesisEquality,
rename,
setElimination,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution,
voidElimination,
independent_pairFormation,
independent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}b,a,a',c,c':Point. (a\_b\_c {}\mRightarrow{} out(b aa') {}\mRightarrow{} out(b cc') {}\mRightarrow{} a'\_b\_c')
Date html generated:
2017_10_02-PM-06_27_20
Last ObjectModification:
2017_08_05-PM-04_20_42
Theory : euclidean!plane!geometry
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