### Nuprl Lemma : pairwise_wf

`∀[T:Type]. ∀[L:T List]. ∀[P:T ⟶ T ⟶ ℙ'].  ((∀x,y∈L.  P[x;y]) ∈ ℙ')`

Proof

Definitions occuring in Statement :  pairwise: `(∀x,y∈L.  P[x; y])` 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 :  pairwise: `(∀x,y∈L.  P[x; y])` uall: `∀[x:A]. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` int_seg: `{i..j-}` so_apply: `x[s1;s2]` 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` so_apply: `x[s]`
Lemmas referenced :  list_wf int_formula_prop_less_lemma intformless_wf decidable__lt int_formula_prop_wf 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 itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le int_seg_properties select_wf length_wf int_seg_wf all_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut thin instantiate lemma_by_obid sqequalHypSubstitution isectElimination natural_numberEquality cumulativity hypothesisEquality hypothesis applyEquality lambdaEquality universeEquality because_Cache setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll imageElimination axiomEquality equalityTransitivity equalitySymmetry functionEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[P:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}'].    ((\mforall{}x,y\mmember{}L.    P[x;y])  \mmember{}  \mBbbP{}')

Date html generated: 2016_05_14-PM-01_49_04
Last ObjectModification: 2016_01_15-AM-08_18_02

Theory : list_1

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