Nuprl Lemma : decidable__list-closed2
∀[T:Type]. ∀L:T List. ∀f:T ⟶ (T List). ∀d:EqDecider(T). Dec(list-closed(T;L;f))
Proof
Definitions occuring in Statement :
list-closed: list-closed(T;L;f),
list: T List,
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q
Lemmas referenced :
decidable__list-closed,
decidable-equal-deq,
deq_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,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
Error :inhabitedIsType,
Error :universeIsType,
Error :functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}f:T {}\mrightarrow{} (T List). \mforall{}d:EqDecider(T). Dec(list-closed(T;L;f))
Date html generated:
2019_06_20-PM-02_13_25
Last ObjectModification:
2019_06_20-PM-02_08_00
Theory : list_1
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