Nuprl Lemma : WfdSpread-ext

∀[Pos:Type]
  ∀[Mv:Pos ⟶ Type]. WfdSpread(Pos;a.Mv[a]) ≡ a:Pos × (Mv[a] ⟶ WfdSpread(Pos;a.Mv[a])) 
  supposing ∀a,b:Pos.  Dec(a = b ∈ Pos)


Proof



Definitions occuring in Statement :  WfdSpread: WfdSpread(Pos;a.Mv[a]),  ext-eq: A ≡ B,  decidable: Dec(P),  uimplies: b supposing a,  uall: ∀[x:A]. B[x],  so_apply: x[s],  all: ∀x:A. B[x],  function: x:A ⟶ B[x],  product: x:A × B[x],  universe: Type,  equal: s = t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  uimplies: b supposing a,  ext-eq: A ≡ B,  and: P ∧ Q,  subtype_rel: A ⊆r B,  so_lambda: λ2x.t[x],  so_apply: x[s],  all: ∀x:A. B[x],  prop: ℙ,  WfdSpread: WfdSpread(Pos;a.Mv[a]),  guard: {T},  implies: P ⇒ Q,  exists: ∃x:A. B[x],  squash: ↓T,  nat: ℕ,  le: A ≤ B,  less_than': less_than'(a;b),  false: False,  not: ¬A,  iff: P ⇐⇒ Q,  rev_implies: P ⇐ Q,  exposed-bfalse: exposed-bfalse,  bool: 𝔹,  unit: Unit,  it: ⋅,  btrue: tt,  ifthenelse: if b then t else f fi ,  uiff: uiff(P;Q),  MoveChoice: MoveChoice(Pos;a.Mv[a]),  eqof: eqof(d),  bfalse: ff,  or: P ∨ Q,  sq_type: SQType(T),  bnot: ¬bb,  assert: ↑b,  ge: i ≥ j ,  int_upper: {i...},  decidable: Dec(P),  satisfiable_int_formula: satisfiable_int_formula(fmla),  top: Top,  subgame: subgame(g;p;n),  eq_int: (i =z j),  subtract: n - m,  resigned: resigned(x),  isr: isr(x),  deq: EqDecider(T),  int_seg: {i..j-},  lelt: i ≤ j < k,  true: True
Lemmas referenced :  spread-ext,  WfdSpread_wf,  decidable_wf,  equal_wf,  subtype_rel_weakening,  Spread_wf,  nat_wf,  MoveChoice_wf,  squash_wf,  exists_wf,  resigned_wf,  subgame_wf,  subtype_rel_function,  int_seg_wf,  int_seg_subtype_nat,  false_wf,  subtype_rel_self,  deq-exists,  eq_int_wf,  eqtt_to_assert,  assert_of_eq_int,  safe-assert-deq,  subtype_rel-equal,  unit_wf2,  eqff_to_assert,  bool_cases_sqequal,  subtype_base_sq,  bool_subtype_base,  assert-bnot,  iff_weakening_uiff,  bool_wf,  neg_assert_of_eq_int,  upper_subtype_nat,  nat_properties,  nequal-le-implies,  zero-add,  le_wf,  subtract_wf,  int_upper_properties,  decidable__le,  full-omega-unsat,  intformand_wf,  intformnot_wf,  intformle_wf,  itermConstant_wf,  itermSubtract_wf,  itermVar_wf,  istype-int,  int_formula_prop_and_lemma,  istype-void,  int_formula_prop_not_lemma,  int_formula_prop_le_lemma,  int_term_value_constant_lemma,  int_term_value_subtract_lemma,  int_term_value_var_lemma,  int_formula_prop_wf,  assert_wf,  bnot_wf,  not_wf,  equal-wf-T-base,  set_subtype_base,  int_subtype_base,  bool_cases,  iff_transitivity,  assert_of_bnot,  eqof_wf,  member_wf,  intformeq_wf,  int_formula_prop_eq_lemma,  true_wf,  decidable__equal_int,  int_seg_properties,  itermAdd_wf,  int_term_value_add_lemma,  add-subtract-cancel,  bfalse_wf,  btrue_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  Error :isect_memberFormation_alt,  introduction,  cut,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  independent_pairFormation,  Error :lambdaEquality_alt,  Error :universeIsType,  sqequalRule,  applyEquality,  hypothesis,  Error :productIsType,  Error :functionIsType,  because_Cache,  productElimination,  independent_pairEquality,  axiomEquality,  Error :inhabitedIsType,  Error :isect_memberEquality_alt,  equalityTransitivity,  equalitySymmetry,  universeEquality,  setElimination,  rename,  cumulativity,  functionExtensionality,  productEquality,  functionEquality,  independent_isectElimination,  Error :lambdaFormation_alt,  Error :dependent_pairEquality_alt,  Error :equalityIsType1,  dependent_functionElimination,  independent_functionElimination,  Error :functionExtensionality_alt,  Error :dependent_set_memberEquality_alt,  imageElimination,  imageMemberEquality,  baseClosed,  natural_numberEquality,  unionElimination,  equalityElimination,  Error :inlEquality_alt,  Error :dependent_pairFormation_alt,  promote_hyp,  instantiate,  voidElimination,  Error :inrEquality_alt,  hypothesis_subsumption,  approximateComputation,  int_eqEquality,  intEquality,  Error :equalityIsType4,  hyp_replacement,  Error :unionIsType,  addEquality,  applyLambdaEquality
Latex:
\mforall{}[Pos:Type]
    \mforall{}[Mv:Pos  {}\mrightarrow{}  Type].  WfdSpread(Pos;a.Mv[a])  \mequiv{}  a:Pos  \mtimes{}  (Mv[a]  {}\mrightarrow{}  WfdSpread(Pos;a.Mv[a])) 
    supposing  \mforall{}a,b:Pos.    Dec(a  =  b)


Date html generated: 2019_06_20-PM-02_02_59
Last ObjectModification: 2018_09_30-PM-02_47_30

Theory : spread


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