### Nuprl Lemma : is-list-approx_wf

`∀T:Type. ∀j:ℕ.  (is-list-approx(j) ∈ colist(T) ⟶ partial(𝔹))`

Proof

Definitions occuring in Statement :  is-list-approx: `is-list-approx(j)` colist: `colist(T)` partial: `partial(T)` nat: `ℕ` bool: `𝔹` all: `∀x:A. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  is-list-approx: `is-list-approx(j)` 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` so_lambda: `λ2x.t[x]` so_apply: `x[s]` bool: `𝔹` decidable: `Dec(P)` or: `P ∨ Q` nat_plus: `ℕ+`
Lemmas referenced :  nat_wf is-list-fun_wf fun_exp_unroll_1 int_term_value_subtract_lemma int_formula_prop_not_lemma itermSubtract_wf intformnot_wf subtract_wf decidable__le unit_wf2 union-value-type bool_wf colist_wf bottom_wf_function fun_exp0_lemma less_than_wf ge_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf satisfiable-full-omega-tt nat_properties
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename introduction intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry cumulativity because_Cache unionElimination dependent_set_memberEquality applyEquality universeEquality

Latex:
\mforall{}T:Type.  \mforall{}j:\mBbbN{}.    (is-list-approx(j)  \mmember{}  colist(T)  {}\mrightarrow{}  partial(\mBbbB{}))

Date html generated: 2016_05_15-PM-10_09_51
Last ObjectModification: 2016_01_11-PM-06_09_24

Theory : eval!all

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