### Nuprl Lemma : descending_wf

`∀[A:Type]. ∀[<:A ⟶ A ⟶ ℙ]. ∀[L:A List].  (descending(a,b.<[a;b];L) ∈ ℙ)`

Proof

Definitions occuring in Statement :  descending: `descending(a,b.<[a; b];L)` list: `T List` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` descending: `descending(a,b.<[a; b];L)` so_lambda: `λ2x.t[x]` so_apply: `x[s1;s2]` int_seg: `{i..j-}` uimplies: `b supposing a` guard: `{T}` lelt: `i ≤ j < k` and: `P ∧ Q` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `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` less_than: `a < b` squash: `↓T` uiff: `uiff(P;Q)` so_apply: `x[s]`
Lemmas referenced :  list_wf false_wf int_term_value_subtract_lemma int_formula_prop_less_lemma itermSubtract_wf intformless_wf subtract-is-int-iff decidable__lt int_formula_prop_wf int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermAdd_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le int_seg_properties select_wf length_wf subtract_wf int_seg_wf all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality cumulativity hypothesisEquality hypothesis lambdaEquality applyEquality because_Cache addEquality setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll pointwiseFunctionality equalityTransitivity equalitySymmetry promote_hyp imageElimination baseApply closedConclusion baseClosed axiomEquality functionEquality universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[<:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[L:A  List].    (descending(a,b.<[a;b];L)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-04_16_33
Last ObjectModification: 2016_01_16-AM-11_07_51

Theory : general

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