Nuprl Lemma : geo-parallel_wf
∀e:EuclideanPlane. ∀a,b,c,d:Point. (geo-parallel(e;a;b;c;d) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-parallel: geo-parallel(e;a;b;c;d),
euclidean-plane: EuclideanPlane,
geo-point: Point,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
geo-parallel: geo-parallel(e;a;b;c;d),
prop: ℙ,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
geo-sep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
all_wf,
geo-point_wf,
geo-colinear_wf,
geo-lsep_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
productEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
because_Cache,
lambdaEquality,
functionEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (geo-parallel(e;a;b;c;d) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_13_10
Last ObjectModification:
2017_10_12-AM-11_07_17
Theory : euclidean!plane!geometry
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