Nuprl Lemma : fset-constrained-image_wf
∀[T,A:Type]. ∀[domeq:EqDecider(T)]. ∀[rngeq:EqDecider(A)]. ∀[f:T ⟶ A]. ∀[P:A ⟶ 𝔹]. ∀[s:fset(T)].
(f"(s) s.t. P ∈ fset(A))
Proof
Definitions occuring in Statement :
fset-constrained-image: f"(s) s.t. P,
fset: fset(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-constrained-image: f"(s) s.t. P,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
f-union_wf,
ifthenelse_wf,
fset_wf,
fset-singleton_wf,
empty-fset_wf,
bool_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T,A:Type]. \mforall{}[domeq:EqDecider(T)]. \mforall{}[rngeq:EqDecider(A)]. \mforall{}[f:T {}\mrightarrow{} A]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[s:fset(T)].
(f"(s) s.t. P \mmember{} fset(A))
Date html generated:
2016_05_14-PM-03_44_21
Last ObjectModification:
2015_12_26-PM-06_38_37
Theory : finite!sets
Home
Index