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: List bool: 𝔹 uall: [x:A]. B[x] prop: all: x:A. B[x] implies:  Q apply: 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:  Q member: t ∈ T prop: subtype_rel: A ⊆B so_lambda: λ2x.t[x] so_apply: x[s] uimplies: 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!


Home Index