Nuprl Lemma : geo-intersect_wf
∀[e:EuclideanPlane]. ∀[p,l:LINE]. (p \/ l ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-intersect: L \/ M,
geoline: LINE,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geoline: LINE,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
geo-intersect: L \/ M,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
geo-line: Line,
pi1: fst(t),
pi2: snd(t),
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
subtype_quotient,
geo-line_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-line-eq_wf,
geo-line-eq-equiv,
exists_wf,
equal_wf,
geoline_wf,
geo-point_wf,
geo-incident_wf,
geo-left_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
lambdaEquality,
because_Cache,
productEquality,
setEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
setElimination,
rename,
productElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[p,l:LINE]. (p \mbackslash{}/ l \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-01_05_12
Last ObjectModification:
2018_05_10-PM-04_45_39
Theory : euclidean!plane!geometry
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