Nuprl Lemma : mk_lambdas-sqequal-n

∀[F1,F2:Base].  ∀n,m:ℕ.  ((F1 ~n F2) ⇒ (mk_lambdas(F1;m) ~n + m mk_lambdas(F2;m)))


Proof



Definitions occuring in Statement :  mk_lambdas: mk_lambdas(F;m),  nat: ℕ,  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  implies: P ⇒ Q,  add: n + m,  base: Base,  sqequal_n: s ~n t
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  all: ∀x:A. B[x],  implies: P ⇒ Q,  nat: ℕ,  false: False,  ge: i ≥ j ,  uimplies: b supposing a,  not: ¬A,  satisfiable_int_formula: satisfiable_int_formula(fmla),  exists: ∃x:A. B[x],  top: Top,  and: P ∧ Q,  prop: ℙ,  mk_lambdas: mk_lambdas(F;m),  bool: 𝔹,  unit: Unit,  it: ⋅,  btrue: tt,  uiff: uiff(P;Q),  ifthenelse: if b then t else f fi ,  bfalse: ff,  subtype_rel: A ⊆r B,  or: P ∨ Q,  sq_type: SQType(T),  guard: {T},  bnot: ¬bb,  assert: ↑b,  rev_implies: P ⇐ Q,  iff: P ⇐⇒ Q,  decidable: Dec(P),  subtract: n - m,  squash: ↓T,  true: True
Lemmas referenced :  nat_properties,  full-omega-unsat,  intformand_wf,  intformle_wf,  itermConstant_wf,  itermVar_wf,  intformless_wf,  istype-int,  int_formula_prop_and_lemma,  istype-void,  int_formula_prop_le_lemma,  int_term_value_constant_lemma,  int_term_value_var_lemma,  int_formula_prop_less_lemma,  int_formula_prop_wf,  ge_wf,  less_than_wf,  add-zero,  primrec0_lemma,  subtract-1-ge-0,  sqequal_n_wf,  nat_wf,  base_wf,  lt_int_wf,  eqtt_to_assert,  assert_of_lt_int,  eqff_to_assert,  int_subtype_base,  bool_cases_sqequal,  subtype_base_sq,  bool_wf,  bool_subtype_base,  assert-bnot,  iff_weakening_uiff,  assert_wf,  decidable__lt,  add-swap,  add-commutes,  add-associates,  squash_wf,  true_wf,  decidable__le,  intformnot_wf,  itermAdd_wf,  itermSubtract_wf,  int_formula_prop_not_lemma,  int_term_value_add_lemma,  int_term_value_subtract_lemma,  le_wf,  subtype_rel_self,  primrec-unroll
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation_alt,  introduction,  cut,  lambdaFormation_alt,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  hypothesis,  setElimination,  rename,  intWeakElimination,  natural_numberEquality,  independent_isectElimination,  approximateComputation,  independent_functionElimination,  dependent_pairFormation_alt,  lambdaEquality_alt,  int_eqEquality,  dependent_functionElimination,  isect_memberEquality_alt,  voidElimination,  sqequalRule,  independent_pairFormation,  universeIsType,  axiomSqequalN,  functionIsTypeImplies,  inhabitedIsType,  because_Cache,  unionElimination,  equalityElimination,  equalityTransitivity,  equalitySymmetry,  productElimination,  equalityIsType2,  baseApply,  closedConclusion,  baseClosed,  applyEquality,  promote_hyp,  instantiate,  cumulativity,  addEquality,  sqequal_n rule,  hyp_replacement,  minusEquality,  imageElimination,  dependent_set_memberEquality_alt,  imageMemberEquality,  universeEquality,  sqequalZero,  equalityIsType1
Latex:
\mforall{}[F1,F2:Base].    \mforall{}n,m:\mBbbN{}.    ((F1  \msim{}n  F2)  {}\mRightarrow{}  (mk\_lambdas(F1;m)  \msim{}n  +  m  mk\_lambdas(F2;m)))


Date html generated: 2019_10_15-AM-10_58_59
Last ObjectModification: 2018_10_11-PM-11_06_04

Theory : untyped!computation


Home Index