Nuprl Lemma : decidable__list-closed2-ext
∀[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 :
member: t ∈ T,
deq-witness: deq-witness(eq),
ifthenelse: if b then t else f fi ,
list_ind: list_ind,
bottom: ⊥,
genrec-ap: genrec-ap,
spreadn: spread3,
decidable__list-closed2,
decidable__list-closed,
decidable-equal-deq,
decidable__l_all,
decidable__l_member,
list_induction,
decidable_functionality,
nil_member,
decidable__false,
cons_member,
decidable__or,
iff_preserves_decidability,
any: any x,
decidable__assert,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
decidable__list-closed2,
lifting-strict-decide,
istype-void,
strict4-decide,
decidable__list-closed,
decidable-equal-deq,
decidable__l_all,
decidable__l_member,
list_induction,
decidable_functionality,
nil_member,
decidable__false,
cons_member,
decidable__or,
iff_preserves_decidability,
decidable__assert
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
independent_isectElimination
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-01_51_21
Last ObjectModification:
2019_05_13-PM-03_38_11
Theory : list_1
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