Nuprl Lemma : l_contains_append2

∀[T:Type]. ∀A,B:T List.  A ⊆ B @ A


Proof




Definitions occuring in Statement :  l_contains: A ⊆ B,  append: as @ bs,  list: T List,  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  universe: Type
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  l_contains: A ⊆ B,  member: t ∈ T,  so_lambda: λ2x.t[x],  prop: ℙ,  so_apply: x[s],  iff: P ⇐⇒ Q,  and: P ∧ Q,  rev_implies: P ⇐ Q,  implies: P ⇒ Q,  guard: {T},  or: P ∨ Q
Lemmas referenced :  l_all_iff,  l_member_wf,  append_wf,  member_append,  all_wf,  or_wf,  list_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation,  lambdaFormation,  cut,  introduction,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  dependent_functionElimination,  sqequalRule,  lambdaEquality,  setElimination,  rename,  hypothesis,  setEquality,  productElimination,  independent_functionElimination,  inrFormation,  because_Cache,  addLevel,  functionEquality,  universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}A,B:T  List.    A  \msubseteq{}  B  @  A



Date html generated: 2019_06_20-PM-01_26_48
Last ObjectModification: 2018_08_24-PM-11_16_44

Theory : list_1


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