Nuprl Lemma : rceq_wf
∀[k:ℕ]. ∀[a,b:ℚCube(k)]. (rceq(k;a;b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
rceq: rceq(k;a;b),
rational-cube: ℚCube(k),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
deq: EqDecider(T),
subtype_rel: A ⊆r B,
rceq: rceq(k;a;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
rc-deq_wf
Rules used in proof :
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
axiomEquality,
equalitySymmetry,
equalityTransitivity,
inhabitedIsType,
rename,
setElimination,
lambdaEquality_alt,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
applyEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[a,b:\mBbbQ{}Cube(k)]. (rceq(k;a;b) \mmember{} \mBbbB{})
Date html generated:
2019_10_29-AM-07_49_15
Last ObjectModification:
2019_10_28-AM-10_59_46
Theory : rationals
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