Nuprl Lemma : rc-deq_wf
∀[k:ℕ]. (rc-deq(k) ∈ EqDecider(ℚCube(k)))
Proof
Definitions occuring in Statement :
rc-deq: rc-deq(k),
rational-cube: ℚCube(k),
deq: EqDecider(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
rational-cube: ℚCube(k),
subtype_rel: A ⊆r B,
rc-deq: rc-deq(k),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
deq_wf,
subtype_rel_self,
ri-deq_wf,
rational-interval_wf,
Error :finite-fun-deq_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesisEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. (rc-deq(k) \mmember{} EqDecider(\mBbbQ{}Cube(k)))
Date html generated:
2019_10_29-AM-07_48_56
Last ObjectModification:
2019_10_18-PM-00_04_31
Theory : rationals
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