Nuprl Lemma : geo-between-exchange4
∀e:BasicGeometry-. ∀[a,b,c,d:Point].  (a_b_d) supposing (a_c_d and a_b_c)
Proof
Definitions occuring in Statement : 
basic-geometry-: BasicGeometry-
, 
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 : 
rev_implies: P 
⇐ Q
, 
and: P ∧ Q
, 
iff: P 
⇐⇒ Q
, 
geo-eq: a ≡ b
, 
false: False
, 
or: P ∨ Q
, 
not: ¬A
, 
stable: Stable{P}
, 
implies: P 
⇒ Q
, 
basic-geometry-: BasicGeometry-
, 
guard: {T}
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
Lemmas referenced : 
minimal-not-not-excluded-middle, 
geo-eq_weakening, 
geo-between_functionality, 
minimal-double-negation-hyp-elim, 
not_wf, 
geo-sep_wf, 
or_wf, 
false_wf, 
stable__geo-between, 
geo-point_wf, 
Error :basic-geo-primitives_wf, 
Error :basic-geo-structure_wf, 
basic-geometry-_wf, 
subtype_rel_transitivity, 
basic-geometry--subtype, 
geo-between_wf, 
geo-between-outer-trans, 
geo-between-exchange3, 
geo-between-inner-trans, 
geo-between-symmetry, 
geo-sep-sym
Rules used in proof : 
productElimination, 
voidElimination, 
unionElimination, 
independent_functionElimination, 
functionEquality, 
rename, 
setElimination, 
dependent_functionElimination, 
because_Cache, 
sqequalRule, 
independent_isectElimination, 
instantiate, 
hypothesis, 
applyEquality, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
cut, 
isect_memberFormation, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry-.  \mforall{}[a,b,c,d:Point].    (a\_b\_d)  supposing  (a\_c\_d  and  a\_b\_c)
Date html generated:
2017_10_02-PM-04_51_37
Last ObjectModification:
2017_08_05-AM-09_08_22
Theory : euclidean!plane!geometry
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