Nuprl Lemma : rat-cube-intersection_wf
∀[k:ℕ]. ∀[c,d:ℚCube(k)]. (c ⋂ d ∈ ℚCube(k))
Proof
Definitions occuring in Statement :
rat-cube-intersection: c ⋂ d,
rational-cube: ℚCube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
nat: ℕ,
rational-cube: ℚCube(k),
rat-cube-intersection: c ⋂ d,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
subtype_rel_self,
int_seg_wf,
rat-interval-intersection_wf
Rules used in proof :
isectIsTypeImplies,
isect_memberEquality_alt,
inhabitedIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
rename,
setElimination,
natural_numberEquality,
universeIsType,
hypothesis,
hypothesisEquality,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaEquality_alt,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c,d:\mBbbQ{}Cube(k)]. (c \mcap{} d \mmember{} \mBbbQ{}Cube(k))
Date html generated:
2019_10_29-AM-07_51_12
Last ObjectModification:
2019_10_17-PM-01_32_16
Theory : rationals
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