### Nuprl Lemma : fps-one-slice

`∀[X:Type]. ∀[r:CRng]. ∀[n:ℤ].  ([1]_n = if (n =z 0) then 1 else 0 fi  ∈ PowerSeries(X;r))`

Proof

Definitions occuring in Statement :  fps-slice: `[f]_n` fps-one: `1` fps-zero: `0` power-series: `PowerSeries(X;r)` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` uall: `∀[x:A]. B[x]` natural_number: `\$n` int: `ℤ` universe: `Type` equal: `s = t ∈ T` crng: `CRng`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` all: `∀x:A. B[x]` fps-zero: `0` fps-one: `1` fps-coeff: `f[b]` fps-slice: `[f]_n` subtype_rel: `A ⊆r B` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` nat: `ℕ` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` nequal: `a ≠ b ∈ T ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` crng: `CRng` rng: `Rng`
Lemmas referenced :  fps-ext fps-slice_wf fps-one_wf ifthenelse_wf eq_int_wf power-series_wf fps-zero_wf bag-size_wf bool_wf eqtt_to_assert assert_of_eq_int nat_wf bag-null_wf assert-bag-null eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot equal-wf-T-base bag_wf neg_assert_of_eq_int bag_size_empty_lemma satisfiable-full-omega-tt intformand_wf intformeq_wf itermVar_wf itermConstant_wf intformnot_wf int_formula_prop_and_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_not_lemma int_formula_prop_wf rng_zero_wf crng_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality cumulativity hypothesis natural_numberEquality productElimination independent_isectElimination lambdaFormation sqequalRule applyEquality because_Cache unionElimination equalityElimination equalityTransitivity equalitySymmetry lambdaEquality setElimination rename dependent_functionElimination dependent_pairFormation promote_hyp instantiate independent_functionElimination voidElimination baseClosed hyp_replacement applyLambdaEquality intEquality int_eqEquality isect_memberEquality voidEquality independent_pairFormation computeAll axiomEquality universeEquality

Latex:
\mforall{}[X:Type].  \mforall{}[r:CRng].  \mforall{}[n:\mBbbZ{}].    ([1]\_n  =  if  (n  =\msubz{}  0)  then  1  else  0  fi  )

Date html generated: 2018_05_21-PM-09_56_00
Last ObjectModification: 2017_07_26-PM-06_32_51

Theory : power!series

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