### Nuprl Lemma : rep-seq-from-0

`∀[T:Type]. ∀[s:ℕ0 ⟶ T]. ∀[f:ℕ ⟶ T].  (rep-seq-from(s;0;f) = f ∈ (ℕ ⟶ T))`

Proof

Definitions occuring in Statement :  rep-seq-from: `rep-seq-from(s;n;f)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` rep-seq-from: `rep-seq-from(s;n;f)` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` bfalse: `ff` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b`
Lemmas referenced :  lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf nat_properties satisfiable-full-omega-tt intformand_wf intformless_wf itermVar_wf itermConstant_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot nat_wf int_seg_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut functionExtensionality sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache lessCases sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination computeAll promote_hyp instantiate cumulativity applyEquality functionEquality axiomEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[s:\mBbbN{}0  {}\mrightarrow{}  T].  \mforall{}[f:\mBbbN{}  {}\mrightarrow{}  T].    (rep-seq-from(s;0;f)  =  f)

Date html generated: 2017_04_20-AM-07_21_05
Last ObjectModification: 2017_02_27-PM-05_56_25

Theory : continuity

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