### Nuprl Lemma : list-match_wf

`∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ]. ∀[as:A List]. ∀[bs:B List].  (list-match(as;bs;a,b.R[a;b]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  list-match: `list-match(L1;L2;a,b.R[a; b])` 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` list-match: `list-match(L1;L2;a,b.R[a; b])` so_lambda: `λ2x.t[x]` prop: `ℙ` and: `P ∧ Q` so_apply: `x[s1;s2]` int_seg: `{i..j-}` uimplies: `b supposing a` guard: `{T}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` implies: `P `` Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` less_than: `a < b` squash: `↓T` subtype_rel: `A ⊆r B` ge: `i ≥ j ` nat: `ℕ` so_apply: `x[s]`
Lemmas referenced :  sq_exists_wf int_seg_wf length_wf inject_wf all_wf select_wf int_seg_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf decidable__lt intformless_wf int_formula_prop_less_lemma non_neg_length lelt_wf length_wf_nat nat_properties list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin functionEquality natural_numberEquality cumulativity hypothesisEquality hypothesis because_Cache lambdaEquality productEquality functionExtensionality applyEquality setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation imageElimination dependent_set_memberEquality equalityTransitivity equalitySymmetry applyLambdaEquality axiomEquality universeEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[R:A  {}\mrightarrow{}  B  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[as:A  List].  \mforall{}[bs:B  List].    (list-match(as;bs;a,b.R[a;b])  \mmember{}  \mBbbP{})

Date html generated: 2018_05_21-PM-00_45_53
Last ObjectModification: 2018_05_19-AM-06_49_10

Theory : list_1

Home Index