Nuprl Lemma : dp-perp_wf
∀[d:DualPlanePrimitives]. ∀[x,y:Vec]. ((x ⊥ y) ∈ ℙ)
Proof
Definitions occuring in Statement :
dp-perp: (x ⊥ y),
dp-vec: Vec,
dual-plane-primitives: DualPlanePrimitives,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dual-plane-primitives: DualPlanePrimitives,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
guard: {T},
prop: ℙ,
dp-perp: (x ⊥ y),
dp-vec: Vec
Lemmas referenced :
subtype_rel_self,
subtype_rel_universe1,
dp-vec_wf,
dual-plane-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesisEquality,
sqequalHypSubstitution,
dependentIntersectionElimination,
sqequalRule,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
extract_by_obid,
isectElimination,
universeEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
closedConclusion,
axiomEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[d:DualPlanePrimitives]. \mforall{}[x,y:Vec]. ((x \mbot{} y) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-AM-11_29_24
Last ObjectModification:
2018_10_16-AM-10_36_08
Theory : matrices
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