Nuprl Lemma : deq-fset_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. (deq-fset(eq) ∈ EqDecider(fset(T)))
Proof
Definitions occuring in Statement :
deq-fset: deq-fset(eq),
fset: fset(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
deq-fset: deq-fset(eq),
member: t ∈ T,
uall: ∀[x:A]. B[x],
decidable__equal_fset,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
top: Top,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable_functionality,
iff_preserves_decidability,
decidable__and2,
decidable__f-subset,
decidable__all_fset,
iff_weakening_uiff,
decidable__fset-member,
assert-deq-fset-member,
decidable__assert,
fset-all-iff,
fset-null: fset-null(s),
null: null(as),
fset-filter: {x ∈ s | P[x]},
filter: filter(P;l),
reduce: reduce(f;k;as),
list_ind: list_ind,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
so_lambda: λ2x.t[x],
so_apply: x[s],
isl: isl(x),
decidable__and,
rev_implies: P ⇐ Q,
false: False,
not: ¬A,
bfalse: ff,
true: True,
btrue: tt,
assert: ↑b,
and: P ∧ Q,
iff: P ⇐⇒ Q,
or: P ∨ Q,
decidable: Dec(P),
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
deq: EqDecider(T)
Lemmas referenced :
deq_wf,
lifting-strict-spread,
istype-void,
strict4-apply,
lifting-strict-decide,
strict4-decide,
iff_wf,
assert_wf,
not_wf,
isl_wf,
all_wf,
deq_subtype2,
fset_wf,
equal_wf,
decidable_wf,
decidable__equal_fset,
decidable_functionality,
iff_preserves_decidability,
decidable__and2,
decidable__f-subset,
decidable__all_fset,
iff_weakening_uiff,
decidable__fset-member,
assert-deq-fset-member,
decidable__assert,
fset-all-iff,
decidable__and
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
extract_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
independent_isectElimination,
natural_numberEquality,
unionElimination,
independent_pairFormation,
independent_functionElimination,
dependent_functionElimination,
functionExtensionality,
lambdaFormation,
functionEquality,
isectEquality,
instantiate,
applyEquality,
lambdaEquality,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. (deq-fset(eq) \mmember{} EqDecider(fset(T)))
Date html generated:
2019_06_20-PM-01_59_25
Last ObjectModification:
2019_01_17-AM-09_39_28
Theory : finite!sets
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