### Nuprl Lemma : co-alt_wf

`co-alt() ∈ colist(ℤ)`

Proof

Definitions occuring in Statement :  co-alt: `co-alt()` colist: `colist(T)` member: `t ∈ T` int: `ℤ`
Definitions unfolded in proof :  colist: `colist(T)` corec: `corec(T.F[T])` member: `t ∈ T` all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` 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` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` subtype_rel: `A ⊆r B` le: `A ≤ B` less_than': `less_than'(a;b)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` co-alt: `co-alt()` b-union: `A ⋃ B` tunion: `⋃x:A.B[x]` ifthenelse: `if b then t else f fi ` bfalse: `ff` subtract: `n - m` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` nequal: `a ≠ b ∈ T ` int_upper: `{i...}` bnot: `¬bb` assert: `↑b` pi2: `snd(t)` 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 int_seg_wf int_seg_properties decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma decidable__equal_int int_seg_subtype false_wf intformeq_wf int_formula_prop_eq_lemma le_wf subtype_base_sq nat_wf set_subtype_base int_subtype_base primrec0_lemma primrec-unroll-1 decidable__lt bfalse_wf lelt_wf bool_wf eqtt_to_assert int_upper_subtype_nat nequal-le-implies zero-add unit_wf2 eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot primrec_wf int_upper_properties top_wf b-union_wf itermAdd_wf int_term_value_add_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberEquality cut thin lambdaFormation introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry because_Cache productElimination unionElimination applyEquality applyLambdaEquality hypothesis_subsumption dependent_set_memberEquality instantiate cumulativity imageMemberEquality dependent_pairEquality independent_pairEquality equalityElimination promote_hyp productEquality universeEquality baseClosed addEquality

Latex:
co-alt()  \mmember{}  colist(\mBbbZ{})

Date html generated: 2018_05_21-PM-10_20_27
Last ObjectModification: 2017_07_26-PM-06_37_28

Theory : eval!all

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