Nuprl Lemma : sq_stable__geo-out
∀e:BasicGeometry. ∀p,a,b:Point. SqStable(out(p ab))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-point: Point,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
geo-out: out(p ab),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane
Lemmas referenced :
sq_stable__and,
geo-sep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
not_wf,
geo-between_wf,
sq_stable__geo-sep,
sq_stable__not,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
isect_memberEquality,
productEquality,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
setElimination,
rename
Latex:
\mforall{}e:BasicGeometry. \mforall{}p,a,b:Point. SqStable(out(p ab))
Date html generated:
2017_10_02-PM-06_26_08
Last ObjectModification:
2017_08_16-PM-06_33_25
Theory : euclidean!plane!geometry
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