Nuprl Lemma : enum-fin-seq-true

`∀m:ℕ. ((λx.tt) = enum-fin-seq(m)[0] ∈ (ℕ ⟶ 𝔹))`

Proof

Definitions occuring in Statement :  enum-fin-seq: `enum-fin-seq(m)` select: `L[n]` nat: `ℕ` btrue: `tt` bool: `𝔹` all: `∀x:A. B[x]` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` enum-fin-seq: `enum-fin-seq(m)` select: `L[n]` cons: `[a / b]` decidable: `Dec(P)` or: `P ∨ Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` squash: `↓T` nequal: `a ≠ b ∈ T ` int_seg: `{i..j-}` true: `True` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` list_n: `A List(n)` lelt: `i ≤ j < k` le: `A ≤ B` less_than': `less_than'(a;b)` nat_plus: `ℕ+` less_than: `a < b`
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf primrec0_lemma btrue_wf nat_wf decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma primrec-unroll eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int squash_wf true_wf select_append_front map_wf primrec_wf list_wf le_wf cons_wf nil_wf append_wf bfalse_wf int_seg_wf iff_weakening_equal length-map enum-fin-seq_wf list_n_wf exp_wf2 false_wf list_n_properties exp-positive-stronger lelt_wf length_wf select-map subtype_rel_list top_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination axiomEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination because_Cache promote_hyp instantiate cumulativity applyEquality imageElimination universeEquality functionEquality functionExtensionality dependent_set_memberEquality imageMemberEquality baseClosed int_eqReduceTrueSq int_eqReduceFalseSq

Latex:
\mforall{}m:\mBbbN{}.  ((\mlambda{}x.tt)  =  enum-fin-seq(m)[0])

Date html generated: 2017_04_20-AM-07_22_41
Last ObjectModification: 2017_02_27-PM-05_59_09

Theory : continuity

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