### Nuprl Lemma : rep-seq-from-prop3

`∀[T:Type]. ∀[n:ℕ]. ∀[s:ℕn ⟶ T]. ∀[f:ℕ ⟶ T].  (rep-seq-from(s.f n@n;n + 1;f) = rep-seq-from(s;n;f) ∈ (ℕ ⟶ T))`

Proof

Definitions occuring in Statement :  rep-seq-from: `rep-seq-from(s;n;f)` seq-add: `s.x@n` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` apply: `f a` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  rep-seq-from: `rep-seq-from(s;n;f)` member: `t ∈ T` uall: `∀[x:A]. B[x]` 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` seq-add: `s.x@n` 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` nequal: `a ≠ b ∈ T ` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)`
Lemmas referenced :  lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf eq_int_wf assert_of_eq_int nat_properties satisfiable-full-omega-tt intformand_wf intformeq_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int int_seg_wf lelt_wf decidable__le intformnot_wf intformle_wf itermConstant_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma le_wf itermAdd_wf int_term_value_add_lemma nat_wf
Rules used in proof :  functionExtensionality sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity sqequalRule cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis addEquality because_Cache natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination lessCases isect_memberFormation sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination independent_functionElimination int_eqReduceTrueSq dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination computeAll promote_hyp instantiate cumulativity int_eqReduceFalseSq applyEquality dependent_set_memberEquality functionEquality universeEquality axiomEquality

Latex:
\mforall{}[T:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[s:\mBbbN{}n  {}\mrightarrow{}  T].  \mforall{}[f:\mBbbN{}  {}\mrightarrow{}  T].    (rep-seq-from(s.f  n@n;n  +  1;f)  =  rep-seq-from(s;n;f))

Date html generated: 2017_04_20-AM-07_21_17
Last ObjectModification: 2017_02_27-PM-05_56_29

Theory : continuity

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