Nuprl Lemma : basic-geo-axioms_wf
∀[g:GeometryPrimitives]. (BasicGeometryAxioms(g) ∈ ℙ)
Proof
Definitions occuring in Statement : 
basic-geo-axioms: BasicGeometryAxioms(g)
, 
geo-primitives: GeometryPrimitives
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
so_apply: x[s]
, 
implies: P 
⇒ Q
, 
so_lambda: λ2x.t[x]
, 
and: P ∧ Q
, 
prop: ℙ
, 
basic-geo-axioms: BasicGeometryAxioms(g)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
geo-primitives_wf, 
geo-lsep_wf, 
geo-congruent_wf, 
geo-between_wf, 
geo-left_wf, 
geo-sep_wf, 
not_wf, 
geo-ge_wf, 
geo-gt-prim_wf, 
geo-point_wf, 
all_wf
Rules used in proof : 
equalitySymmetry, 
equalityTransitivity, 
axiomEquality, 
universeIsType, 
inhabitedIsType, 
functionEquality, 
because_Cache, 
lambdaEquality_alt, 
hypothesis, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
productEquality, 
sqequalRule, 
cut, 
introduction, 
isect_memberFormation_alt, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[g:GeometryPrimitives].  (BasicGeometryAxioms(g)  \mmember{}  \mBbbP{})
Date html generated:
2019_10_29-AM-09_12_51
Last ObjectModification:
2019_10_25-PM-01_58_55
Theory : euclidean!plane!geometry
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