### Nuprl Lemma : replace-seq-from-member-enum

`∀f:ℕ ⟶ 𝔹. ∀m:ℕ.  (replace-seq-from(f;m;tt) ∈ enum-fin-seq(m))`

Proof

Definitions occuring in Statement :  replace-seq-from: `replace-seq-from(s;n;k)` enum-fin-seq: `enum-fin-seq(m)` l_member: `(x ∈ l)` nat: `ℕ` btrue: `tt` bool: `𝔹` all: `∀x:A. B[x]` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` nat: `ℕ` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` and: `P ∧ Q` subtype_rel: `A ⊆r B` list_n: `A List(n)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` enum-fin-seq: `enum-fin-seq(m)` replace-seq-from: `replace-seq-from(s;n;k)` less_than: `a < b` less_than': `less_than'(a;b)` true: `True` squash: `↓T` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ge: `i ≥ j ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` cand: `A c∧ B` nequal: `a ≠ b ∈ T `
Lemmas referenced :  l_member_wf nat_wf bool_wf replace-seq-from_wf decidable__le subtract_wf full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf le_wf btrue_wf enum-fin-seq_wf list_n_wf exp_wf2 set_wf less_than_wf primrec-wf2 primrec0_lemma member_singleton top_wf lt_int_wf eqtt_to_assert assert_of_lt_int nat_properties eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot primrec-unroll squash_wf true_wf list_wf replace-seq-from-succ append_wf map_wf bfalse_wf subtype_rel_self iff_weakening_equal bool_cases implies_l_member_append eq_int_wf assert_of_eq_int iff_imp_equal_bool assert_wf int_subtype_base neg_assert_of_eq_int member-map assert_elim btrue_neq_bfalse false_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut thin rename setElimination introduction extract_by_obid sqequalHypSubstitution isectElimination functionEquality hypothesis functionExtensionality applyEquality hypothesisEquality because_Cache dependent_set_memberEquality dependent_functionElimination natural_numberEquality unionElimination independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation lessCases baseClosed equalityTransitivity equalitySymmetry imageMemberEquality isect_memberFormation axiomSqEquality imageElimination productElimination equalityElimination promote_hyp instantiate cumulativity universeEquality inlFormation int_eqReduceTrueSq int_eqReduceFalseSq productEquality inrFormation addLevel levelHypothesis

Latex:
\mforall{}f:\mBbbN{}  {}\mrightarrow{}  \mBbbB{}.  \mforall{}m:\mBbbN{}.    (replace-seq-from(f;m;tt)  \mmember{}  enum-fin-seq(m))

Date html generated: 2019_06_20-PM-02_57_15
Last ObjectModification: 2018_08_20-PM-09_39_30

Theory : continuity

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