Nuprl Lemma : filter_safety
∀[T:Type]. ∀[P:(T List) ⟶ ℙ]. ∀f:T ⟶ 𝔹. (safety(T;L.P L) ⇒ safety(T;L.P filter(f;L)))
Proof
Definitions occuring in Statement :
safety: safety(A;tr.P[tr]),
filter: filter(P;l),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
safety: safety(A;tr.P[tr]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
filter_wf5,
subtype_rel_dep_function,
bool_wf,
l_member_wf,
subtype_rel_self,
set_wf,
iseg_wf,
list_wf,
all_wf,
filter_iseg
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
applyEquality,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
hypothesis,
setEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[P:(T List) {}\mrightarrow{} \mBbbP{}]. \mforall{}f:T {}\mrightarrow{} \mBbbB{}. (safety(T;L.P L) {}\mRightarrow{} safety(T;L.P filter(f;L)))
Date html generated:
2019_10_15-AM-10_54_06
Last ObjectModification:
2018_09_17-PM-06_40_00
Theory : list!
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