### Nuprl Lemma : accum_list_wf

`∀[T,A:Type]. ∀[base:T ⟶ A]. ∀[f:A ⟶ T ⟶ A]. ∀[L:T List].  accum_list(a,x.f[a;x];x.base[x];L) ∈ A supposing 0 < ||L||`

Proof

Definitions occuring in Statement :  accum_list: `accum_list(a,x.f[a; x];x.base[x];L)` length: `||as||` list: `T List` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s1;s2]` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` accum_list: `accum_list(a,x.f[a; x];x.base[x];L)` so_apply: `x[s]` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` less_than: `a < b` squash: `↓T` and: `P ∧ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]`
Lemmas referenced :  list_wf less_than_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_not_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt length_wf decidable__le hd_wf tl_wf list_accum_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality because_Cache hypothesis applyEquality independent_isectElimination dependent_functionElimination natural_numberEquality unionElimination imageElimination productElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll axiomEquality equalityTransitivity equalitySymmetry functionEquality universeEquality

Latex:
\mforall{}[T,A:Type].  \mforall{}[base:T  {}\mrightarrow{}  A].  \mforall{}[f:A  {}\mrightarrow{}  T  {}\mrightarrow{}  A].  \mforall{}[L:T  List].
accum\_list(a,x.f[a;x];x.base[x];L)  \mmember{}  A  supposing  0  <  ||L||

Date html generated: 2016_05_14-AM-07_39_57
Last ObjectModification: 2016_01_15-AM-08_36_23

Theory : list_1

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