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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