Nuprl Lemma : bounded-type_wf
∀[T:Type]. (Bounded(T) ∈ ℙ)
Proof
Definitions occuring in Statement :
bounded-type: Bounded(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
prop: ℙ,
bounded-type: Bounded(T),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
istype-nat,
le_wf,
sq_exists_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
rename,
setElimination,
applyEquality,
lambdaEquality_alt,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
hypothesisEquality,
functionEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. (Bounded(T) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_20_06
Last ObjectModification:
2019_10_07-PM-04_38_48
Theory : bar-induction
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