Nuprl Lemma : finite-fun-deq_wf
∀[T:Type]. ∀[k:ℕ]. ∀[eq:EqDecider(T)]. (finite-fun-deq(k;eq) ∈ EqDecider(ℕk ⟶ T))
Proof
Definitions occuring in Statement :
finite-fun-deq: finite-fun-deq(k;eq),
deq: EqDecider(T),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
finite-fun-deq: finite-fun-deq(k;eq),
deq: EqDecider(T),
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
eqof: eqof(d),
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a
Lemmas referenced :
bdd-all_wf,
int_seg_wf,
istype-assert,
deq_wf,
istype-nat,
istype-universe,
assert-bdd-all,
eqof_wf,
safe-assert-deq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
applyEquality,
setElimination,
rename,
hypothesis,
universeIsType,
natural_numberEquality,
inhabitedIsType,
functionIsType,
lambdaFormation_alt,
independent_pairFormation,
equalityIstype,
because_Cache,
productIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_isectElimination,
applyLambdaEquality,
functionExtensionality
Latex:
\mforall{}[T:Type]. \mforall{}[k:\mBbbN{}]. \mforall{}[eq:EqDecider(T)]. (finite-fun-deq(k;eq) \mmember{} EqDecider(\mBbbN{}k {}\mrightarrow{} T))
Date html generated:
2020_05_19-PM-09_36_35
Last ObjectModification:
2019_10_18-AM-11_58_52
Theory : equality!deciders
Home
Index