Nuprl Lemma : stable__Playfair-axiom
∀g:EuclideanPlane. Stable{Playfair-axiom(g)}
Proof
Definitions occuring in Statement :
Playfair-axiom: Playfair-axiom(e),
euclidean-plane: EuclideanPlane,
stable: Stable{P},
all: ∀x:A. B[x]
Definitions unfolded in proof :
Playfair-axiom: Playfair-axiom(e),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
so_apply: x[s],
geo-line-eq: l ≡ m
Lemmas referenced :
euclidean-plane_wf,
stable__all,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane-structure_wf,
geo-primitives_wf,
all_wf,
geo-line_wf,
geo-incident_wf,
geoline-subtype1,
geo-Aparallel_wf,
geo-line-eq_wf,
stable__implies,
stable__not,
geo-line-sep_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
independent_isectElimination,
lambdaEquality,
dependent_functionElimination,
because_Cache,
functionEquality,
productEquality,
productElimination,
independent_functionElimination
Latex:
\mforall{}g:EuclideanPlane. Stable\{Playfair-axiom(g)\}
Date html generated:
2018_05_22-PM-01_08_32
Last ObjectModification:
2018_05_11-PM-10_49_35
Theory : euclidean!plane!geometry
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