Nuprl Lemma : rat-sub-cube_wf
∀[k:ℕ]. ∀[a,b:ℚCube(k)]. (rat-sub-cube(k;a;b) ∈ ℙ)
Proof
Definitions occuring in Statement :
rat-sub-cube: rat-sub-cube(k;a;b),
rational-cube: ℚCube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rat-sub-cube: rat-sub-cube(k;a;b),
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
rational-cube: ℚCube(k)
Lemmas referenced :
int_seg_wf,
rat-sub-interval_wf,
rational-cube_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[a,b:\mBbbQ{}Cube(k)]. (rat-sub-cube(k;a;b) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-09_17_43
Last ObjectModification:
2019_11_14-PM-08_04_40
Theory : rationals
Home
Index