Nuprl Lemma : stable__incident
∀e:EuclideanPlane. ∀a:Point. ∀l:LINE. Stable{a I l}
Proof
Definitions occuring in Statement :
geo-incident: p I L,
geoline: LINE,
euclidean-plane: EuclideanPlane,
geo-point: Point,
stable: Stable{P},
all: ∀x:A. B[x]
Definitions unfolded in proof :
geo-incident: p I L,
all: ∀x:A. B[x],
geoline: LINE,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
geo-line: Line,
pi1: fst(t),
pi2: snd(t),
so_apply: x[s],
top: Top
Lemmas referenced :
subtype_quotient,
geo-line_wf,
geo-line-eq_wf,
geo-line-eq-equiv,
stable__all,
equal_wf,
geoline_wf,
geo-colinear_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
stable__implies,
stable__colinear,
pi1_wf_top,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
lambdaEquality,
independent_isectElimination,
functionEquality,
instantiate,
productElimination,
independent_functionElimination,
independent_pairEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a:Point. \mforall{}l:LINE. Stable\{a I l\}
Date html generated:
2018_05_22-PM-01_04_05
Last ObjectModification:
2018_05_10-PM-04_40_16
Theory : euclidean!plane!geometry
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