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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