Nuprl Lemma : decidable__list-closed
∀[T:Type]. ∀L:T List. ∀f:T ⟶ (T List). ((∀x,y:T. Dec(x = y ∈ T)) ⇒ Dec(list-closed(T;L;f)))
Proof
Definitions occuring in Statement :
list-closed: list-closed(T;L;f),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
list-closed: list-closed(T;L;f),
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
decidable__l_all,
l_all_wf,
l_member_wf,
decidable__l_member,
decidable_wf,
equal_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
Error :lambdaEquality_alt,
applyEquality,
setElimination,
rename,
hypothesis,
Error :setIsType,
Error :universeIsType,
independent_functionElimination,
because_Cache,
Error :functionIsType,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}f:T {}\mrightarrow{} (T List). ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} Dec(list-closed(T;L;f)))
Date html generated:
2019_06_20-PM-01_50_58
Last ObjectModification:
2019_05_13-PM-03_36_46
Theory : list_1
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