Nuprl Lemma : geo-line-sep_wf
∀[g:GeometryPrimitives]. ∀[l,m:Line]. (geo-line-sep(g;l;m) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-line-sep: geo-line-sep(g;l;m),
geo-line: Line,
geo-primitives: GeometryPrimitives,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_apply: x[s],
pi2: snd(t),
pi1: fst(t),
geo-line: Line,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
geo-line-sep: geo-line-sep(g;l;m),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-primitives_wf,
geo-line_wf,
geo-lsep_wf,
geo-colinear_wf,
geo-point_wf,
exists_wf
Rules used in proof :
isect_memberEquality,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productElimination,
because_Cache,
productEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:GeometryPrimitives]. \mforall{}[l,m:Line]. (geo-line-sep(g;l;m) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-01_00_15
Last ObjectModification:
2018_05_21-AM-01_32_46
Theory : euclidean!plane!geometry
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