Nuprl Lemma : geo-left-axioms_wf
∀[g:GeometryPrimitives]. (geo-left-axioms(g) ∈ ℙ)
Proof
Definitions occuring in Statement : 
geo-left-axioms: geo-left-axioms(g)
, 
geo-primitives: GeometryPrimitives
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
geo-left-axioms: geo-left-axioms(g)
, 
prop: ℙ
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
Lemmas referenced : 
geo-point_wf, 
iff_wf, 
not_wf, 
geo-lsep_wf, 
geo-colinear_wf, 
geo-left_wf, 
geo-sep_wf, 
geo-between_wf, 
geo-primitives_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
productEquality, 
functionEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeIsType
Latex:
\mforall{}[g:GeometryPrimitives].  (geo-left-axioms(g)  \mmember{}  \mBbbP{})
Date html generated:
2019_10_16-PM-01_12_56
Last ObjectModification:
2019_09_05-AM-10_47_19
Theory : euclidean!plane!geometry
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