Nuprl Lemma : sq_stable__geo-left
∀g:EuclideanPlane. ∀a,b,c:Point. SqStable(a leftof bc)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-left: a leftof bc,
geo-point: Point,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
geo-colinear: Colinear(a;b;c),
and: P ∧ Q,
basic-geo-axioms: BasicGeometryAxioms(g),
false: False,
not: ¬A,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
squash: ↓T,
sq_stable: SqStable(P),
euclidean-plane: EuclideanPlane,
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
sq_stable__not,
geo-colinear_wf,
not_wf,
geo-lsep_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
sq_stable__all,
sq_stable__geo-axioms,
euclidean-plane_wf,
sq_stable__geo-left-1
Rules used in proof :
productElimination,
functionIsTypeImplies,
voidElimination,
inhabitedIsType,
because_Cache,
functionEquality,
lambdaEquality_alt,
applyEquality,
isectElimination,
imageElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
hypothesisEquality,
rename,
setElimination,
universeIsType,
hypothesis,
independent_functionElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point. SqStable(a leftof bc)
Date html generated:
2019_10_30-AM-06_18_25
Last ObjectModification:
2019_10_29-PM-02_46_02
Theory : euclidean!plane!geometry
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