Nuprl Lemma : sq_stable__geo-lsep
∀g:EuclideanPlaneStructure. ∀a,b,c:Point.  SqStable(a # bc)
Proof
Definitions occuring in Statement : 
euclidean-plane-structure: EuclideanPlaneStructure
, 
geo-lsep: a # bc
, 
geo-point: Point
, 
sq_stable: SqStable(P)
, 
all: ∀x:A. B[x]
Definitions unfolded in proof : 
subtype_rel: A ⊆r B
, 
or: P ∨ Q
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
eq_atom: x =a y
, 
record+: record+, 
euclidean-plane-structure: EuclideanPlaneStructure
, 
record-select: r.x
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
geo-lsep: a # bc
Lemmas referenced : 
euclidean-plane-structure_wf, 
geo-left_wf, 
sq_stable_wf, 
geo-point_wf
Rules used in proof : 
universeIsType, 
hyp_replacement, 
lambdaEquality_alt, 
equalitySymmetry, 
equalityTransitivity, 
tokenEquality, 
applyEquality, 
hypothesisEquality, 
unionEquality, 
hypothesis, 
isectElimination, 
extract_by_obid, 
cumulativity, 
functionEquality, 
cut, 
dependentIntersectionEqElimination, 
thin, 
dependentIntersectionElimination, 
sqequalHypSubstitution, 
introduction, 
lambdaFormation_alt, 
computationStep, 
sqequalTransitivity, 
sqequalReflexivity, 
sqequalRule, 
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlaneStructure.  \mforall{}a,b,c:Point.    SqStable(a  \#  bc)
Date html generated:
2019_10_30-AM-06_18_16
Last ObjectModification:
2019_10_29-PM-01_00_33
Theory : euclidean!plane!geometry
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