Nuprl Lemma : geo-line-pt-sep
∀eu:EuclideanPlane. ∀l:Line. fst(l) ≠ fst(snd(l))
Proof
Definitions occuring in Statement :
geo-line: Line,
euclidean-plane: EuclideanPlane,
geo-sep: a ≠ b,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
pi2: snd(t),
pi1: fst(t),
geo-line: Line,
all: ∀x:A. B[x]
Lemmas referenced :
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-line_wf
Rules used in proof :
independent_isectElimination,
isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
hypothesis,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}eu:EuclideanPlane. \mforall{}l:Line. fst(l) \mneq{} fst(snd(l))
Date html generated:
2018_07_29-AM-09_35_32
Last ObjectModification:
2018_06_19-PM-01_24_54
Theory : euclidean!plane!geometry
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