Nuprl Lemma : dl-aprog_wf

∀[x:ℕ]. (atm(x) ∈ Prog)


Proof




Definitions occuring in Statement :  dl-aprog: atm(x),  dl-prog: Prog,  nat: ℕ,  uall: ∀[x:A]. B[x],  member: t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  dl-prog: Prog,  dl-aprog: atm(x),  member: t ∈ T,  subtype_rel: A ⊆r B,  nat: ℕ,  tuple-type: tuple-type(L),  list_ind: list_ind,  prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl),  map: map(f;as),  mrec-spec: mrec-spec(L;lbl;p),  apply-alist: apply-alist(eq;L;x),  dl-Spec: dl-Spec(),  cons: [a / b],  ifthenelse: if b then t else f fi ,  atom-deq: AtomDeq,  eq_atom: x =a y,  pi1: fst(t),  btrue: tt,  pi2: snd(t),  null: null(as),  nil: [],  it: ⋅,  so_lambda: λ2x y.t[x; y],  so_apply: x[s1;s2],  uimplies: b supposing a,  less_than: a < b,  squash: ↓T,  less_than': less_than'(a;b),  length: ||as||,  true: True,  and: P ∧ Q
Lemmas referenced :  mk-prec_wf-mrec,  dl-Spec_wf,  subtype_rel_self,  tuple-type_wf,  prec-arg-types_wf,  mrec-spec_wf,  istype-atom,  istype-nat
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation_alt,  sqequalRule,  cut,  introduction,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesis,  closedConclusion,  tokenEquality,  hypothesisEquality,  applyEquality,  atomEquality,  lambdaEquality_alt,  inhabitedIsType,  independent_isectElimination,  independent_pairFormation,  natural_numberEquality,  imageMemberEquality,  baseClosed

Latex:
\mforall{}[x:\mBbbN{}].  (atm(x)  \mmember{}  Prog)



Date html generated: 2019_10_15-AM-11_39_18
Last ObjectModification: 2019_03_26-AM-11_24_04

Theory : dynamic!logic


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