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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