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: List uall: [x:A]. B[x] prop: 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 ⊆B so_lambda: λ2x.t[x] int_seg: {i..j-} so_apply: x[s1;s2] uimplies: 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:  Q not: ¬A top: Top prop: 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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