Nuprl Lemma : rprod-empty

[n,m:ℤ]. ∀[x:Top].  rprod(n;m;k.x[k]) r1 supposing m < n


Proof




Definitions occuring in Statement :  rprod: rprod(n;m;k.x[k]) int-to-real: r(n) less_than: a < b uimplies: supposing a uall: [x:A]. B[x] top: Top so_apply: x[s] natural_number: $n int: sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a rprod: rprod(n;m;k.x[k]) all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q ifthenelse: if then else fi  bfalse: ff exists: x:A. B[x] or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b false: False not: ¬A rev_implies:  Q iff: ⇐⇒ Q satisfiable_int_formula: satisfiable_int_formula(fmla) top: Top prop:
Lemmas referenced :  lt_int_wf eqtt_to_assert assert_of_lt_int eqff_to_assert bool_cases_sqequal subtype_base_sq bool_wf bool_subtype_base assert-bnot iff_weakening_uiff assert_wf less_than_wf full-omega-unsat intformand_wf intformless_wf itermVar_wf intformnot_wf istype-int int_formula_prop_and_lemma istype-void int_formula_prop_less_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_formula_prop_wf istype-less_than istype-top
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis inhabitedIsType lambdaFormation_alt unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache sqequalRule dependent_pairFormation_alt equalityIstype promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination natural_numberEquality approximateComputation lambdaEquality_alt int_eqEquality isect_memberEquality_alt independent_pairFormation universeIsType axiomSqEquality isectIsTypeImplies

Latex:
\mforall{}[n,m:\mBbbZ{}].  \mforall{}[x:Top].    rprod(n;m;k.x[k])  \msim{}  r1  supposing  m  <  n



Date html generated: 2019_10_29-AM-10_16_42
Last ObjectModification: 2019_01_15-AM-10_03_40

Theory : reals


Home Index