Nuprl Lemma : geo-line-exists
∀g:EuclideanPlane. Line
Proof
Definitions occuring in Statement :
geo-line: Line,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x]
Definitions unfolded in proof :
sq_exists: ∃x:A [B[x]],
prop: ℙ,
exists: ∃x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-line: Line,
all: ∀x:A. B[x]
Lemmas referenced :
equal_wf,
geo-sep-exists,
geo-sep_wf,
sq_exists_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-point_wf,
exists_wf,
geo-nontrivial_wf
Rules used in proof :
productEquality,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
dependent_functionElimination,
dependent_pairFormation,
productElimination,
because_Cache,
lambdaEquality,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlane. Line
Date html generated:
2018_05_22-PM-01_19_13
Last ObjectModification:
2018_01_16-AM-09_54_09
Theory : euclidean!plane!geometry
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