Nuprl Lemma : geo-le_wf
∀[e:BasicGeometry]. ∀[p,q:Length]. (p ≤ q ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-le: p ≤ q,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
subtype-geo-length-type,
geo-length-type_wf,
basic-geometry_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-O_wf,
geo-X_wf,
geo-point_wf,
geo-between_wf,
equal_wf,
squash_wf,
exists_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
applyEquality,
instantiate,
independent_isectElimination,
dependent_functionElimination,
setElimination,
rename,
productEquality,
setEquality,
lambdaEquality
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[p,q:Length]. (p \mleq{} q \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-04_51_59
Last ObjectModification:
2017_08_17-PM-01_31_04
Theory : euclidean!plane!geometry
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