Nuprl Lemma : dist-axiomsA_wf
∀[g:EuclideanPlane]. (dist-axiomsA(g) ∈ ℙ)
Proof
Definitions occuring in Statement :
dist-axiomsA: dist-axiomsA(g),
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dist-axiomsA: dist-axiomsA(g),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
or: P ∨ Q
Lemmas referenced :
all_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
dist_wf,
not_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
lambdaEquality,
because_Cache,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[g:EuclideanPlane]. (dist-axiomsA(g) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-02_44_48
Last ObjectModification:
2018_09_14-PM-08_40_31
Theory : euclidean!plane!geometry
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