Nuprl Lemma : inhabited-rat-cube_wf
∀[k:ℕ]. ∀[c:ℚCube(k)]. (Inhabited(c) ∈ 𝔹)
Proof
Definitions occuring in Statement :
inhabited-rat-cube: Inhabited(c),
rational-cube: ℚCube(k),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
nat: ℕ,
rational-cube: ℚCube(k),
so_lambda: λ2x.t[x],
inhabited-rat-cube: Inhabited(c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
int_seg_wf,
inhabited-rat-interval_wf,
bdd-all_wf
Rules used in proof :
inhabitedIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
rename,
setElimination,
natural_numberEquality,
universeIsType,
hypothesis,
applyEquality,
lambdaEquality_alt,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c:\mBbbQ{}Cube(k)]. (Inhabited(c) \mmember{} \mBbbB{})
Date html generated:
2019_10_29-AM-07_51_36
Last ObjectModification:
2019_10_17-PM-04_36_21
Theory : rationals
Home
Index