### Nuprl Lemma : tuple-equiv_wf

`∀[L:(X:Type × (X ⟶ X ⟶ ℙ)) List]`
`  (tuple-equiv(L) ∈ tuple-type(map(λp.(fst(p));L)) ⟶ tuple-type(map(λp.(fst(p));L)) ⟶ ℙ)`

Proof

Definitions occuring in Statement :  tuple-equiv: `tuple-equiv(L)` tuple-type: `tuple-type(L)` map: `map(f;as)` list: `T List` uall: `∀[x:A]. B[x]` prop: `ℙ` pi1: `fst(t)` member: `t ∈ T` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` product: `x:A × B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` tuple-equiv: `tuple-equiv(L)` let: let prop: `ℙ` so_lambda: `λ2x.t[x]` all: `∀x:A. B[x]` implies: `P `` Q` pi1: `fst(t)` pi2: `snd(t)` subtype_rel: `A ⊆r B` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` cand: `A c∧ B` top: `Top` int_seg: `{i..j-}` lelt: `i ≤ j < k` less_than: `a < b` squash: `↓T` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` label: `...\$L... t` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` select: `L[n]` so_apply: `x[s]`
Lemmas referenced :  all_wf int_seg_wf length_wf select-tuple_wf map_wf istype-universe int_seg_subtype_nat istype-false map-length istype-void int_seg_properties decidable__lt full-omega-unsat intformand_wf intformnot_wf intformless_wf itermVar_wf istype-int int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_formula_prop_wf equal_wf squash_wf true_wf length-map-sq subtype_rel_list top_wf iff_weakening_equal subtype_rel_self select-map tuple-type_wf pi1_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalRule Error :lambdaEquality_alt,  extract_by_obid sqequalHypSubstitution isectElimination thin closedConclusion natural_numberEquality instantiate productEquality universeEquality functionEquality cumulativity hypothesisEquality hypothesis applyEquality because_Cache Error :inhabitedIsType,  Error :lambdaFormation_alt,  productElimination Error :equalityIstype,  equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination Error :productIsType,  Error :functionIsType,  Error :universeIsType,  independent_isectElimination independent_pairFormation Error :isect_memberEquality_alt,  voidElimination setElimination rename imageElimination unionElimination approximateComputation Error :dependent_pairFormation_alt,  int_eqEquality intEquality imageMemberEquality baseClosed axiomEquality

Latex:
\mforall{}[L:(X:Type  \mtimes{}  (X  {}\mrightarrow{}  X  {}\mrightarrow{}  \mBbbP{}))  List]
(tuple-equiv(L)  \mmember{}  tuple-type(map(\mlambda{}p.(fst(p));L))  {}\mrightarrow{}  tuple-type(map(\mlambda{}p.(fst(p));L))  {}\mrightarrow{}  \mBbbP{})

Date html generated: 2019_06_20-PM-02_16_35
Last ObjectModification: 2019_03_18-PM-04_05_25

Theory : tuples

Home Index