### Nuprl Lemma : pair-list

`∀[T:Type]. ∀[L:T List].  L ∈ T × (T List) supposing ispair(L) = tt`

Proof

Definitions occuring in Statement :  list: `T List` bfalse: `ff` btrue: `tt` bool: `𝔹` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` ispair: `if z is a pair then a otherwise b` member: `t ∈ T` product: `x:A × B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` guard: `{T}` or: `P ∨ Q` nil: `[]` it: `⋅` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` decidable: `Dec(P)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)`
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf equal-wf-T-base bool_wf ispair_wf_list nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases btrue_neq_bfalse equal-wf-base product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry cumulativity baseClosed applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination applyLambdaEquality dependent_set_memberEquality addEquality instantiate imageElimination universeEquality independent_pairEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].    L  \mmember{}  T  \mtimes{}  (T  List)  supposing  ispair(L)  =  tt

Date html generated: 2017_04_14-AM-09_25_49
Last ObjectModification: 2017_02_27-PM-03_59_56

Theory : list_1

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