### Nuprl Lemma : has-value-l-last-default-list

`∀[l,d:Base].  l ∈ Top List supposing (l-last-default(l;d))↓`

Proof

Definitions occuring in Statement :  l-last-default: `l-last-default(l;d)` list: `T List` has-value: `(a)↓` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` top: `Top` member: `t ∈ T` base: `Base`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` l-last-default: `l-last-default(l;d)` list_ind: list_ind nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` decidable: `Dec(P)` or: `P ∨ Q` nat_plus: `ℕ+` has-value: `(a)↓` cons: `[a / b]` guard: `{T}` it: `⋅` nil: `[]`
Lemmas referenced :  nil_wf has-value-implies-dec-isaxiom-2 cons_wf top_wf has-value-implies-dec-ispair-2 fun_exp_unroll_1 int_term_value_subtract_lemma int_formula_prop_not_lemma itermSubtract_wf intformnot_wf subtract_wf decidable__le bottom_diverge strictness-apply fun_exp0_lemma base_wf int_subtype_base has-value_wf_base 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 sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution sqequalRule hypothesis compactness thin lemma_by_obid isectElimination hypothesisEquality setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry baseApply closedConclusion baseClosed applyEquality unionElimination dependent_set_memberEquality callbyvalueApply callbyvalueCallbyvalue callbyvalueReduce because_Cache

Latex:
\mforall{}[l,d:Base].    l  \mmember{}  Top  List  supposing  (l-last-default(l;d))\mdownarrow{}

Date html generated: 2016_05_14-AM-07_41_42
Last ObjectModification: 2016_01_15-AM-08_36_29

Theory : list_1

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