Nuprl Lemma : rat-cube-intersection-symm
∀[k:ℕ]. ∀[c,d:ℚCube(k)]. (c ⋂ d = d ⋂ c ∈ ℚCube(k))
Proof
Definitions occuring in Statement :
rat-cube-intersection: c ⋂ d,
rational-cube: ℚCube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
nat: ℕ,
rat-cube-intersection: c ⋂ d,
rational-cube: ℚCube(k),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_seg_wf,
rat-interval-intersection-symm
Rules used in proof :
inhabitedIsType,
isectIsTypeImplies,
axiomEquality,
isect_memberEquality_alt,
because_Cache,
rename,
setElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
functionExtensionality,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c,d:\mBbbQ{}Cube(k)]. (c \mcap{} d = d \mcap{} c)
Date html generated:
2019_10_29-AM-07_51_18
Last ObjectModification:
2019_10_18-PM-00_48_55
Theory : rationals
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