### Nuprl Lemma : nil_interleaving

`∀[T:Type]. ∀L1,L:T List.  (interleaving(T;[];L1;L) `⇐⇒` L = L1 ∈ (T List))`

Proof

Definitions occuring in Statement :  interleaving: `interleaving(T;L1;L2;L)` nil: `[]` list: `T List` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  subtype_rel: `A ⊆r B` rev_implies: `P `` Q` top: `Top` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` uimplies: `b supposing a` uiff: `uiff(P;Q)` or: `P ∨ Q` decidable: `Dec(P)` ge: `i ≥ j ` guard: `{T}` not: `¬A` false: `False` less_than': `less_than'(a;b)` le: `A ≤ B` nat: `ℕ` prop: `ℙ` member: `t ∈ T` implies: `P `` Q` and: `P ∧ Q` iff: `P `⇐⇒` Q` all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` interleaving: `interleaving(T;L1;L2;L)` disjoint_sublists: `disjoint_sublists(T;L1;L2;L)` select: `L[n]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` int_seg: `{i..j-}` lelt: `i ≤ j < k` cand: `A c∧ B` less_than: `a < b` squash: `↓T`
Lemmas referenced :  decidable__equal_int list_wf and_wf non_neg_length nil_wf disjoint_sublists_wf int_formula_prop_wf int_formula_prop_eq_lemma int_term_value_add_lemma 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 intformeq_wf itermAdd_wf itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt add-is-int-iff decidable__le nat_properties le_wf false_wf add_nat_wf length_wf length_wf_nat nat_wf equal_wf length_of_nil_lemma disjoint_sublists_sublist proper_sublist_length stuck-spread istype-base int_seg_properties full-omega-unsat istype-int decidable__lt intformless_wf int_formula_prop_less_lemma istype-le istype-less_than int_seg_wf id_increasing istype-void select_wf increasing_wf
Rules used in proof :  universeEquality hyp_replacement applyEquality because_Cache independent_functionElimination computeAll voidEquality voidElimination isect_memberEquality intEquality int_eqEquality lambdaEquality dependent_pairFormation independent_isectElimination closedConclusion baseApply baseClosed promote_hyp pointwiseFunctionality unionElimination dependent_functionElimination rename setElimination applyLambdaEquality equalitySymmetry equalityTransitivity natural_numberEquality addEquality dependent_set_memberEquality hypothesisEquality cumulativity isectElimination productEquality thin productElimination sqequalHypSubstitution independent_pairFormation lambdaFormation isect_memberFormation hypothesis extract_by_obid introduction cut computationStep sqequalTransitivity sqequalReflexivity sqequalRule sqequalSubstitution lambdaFormation_alt Error :memTop,  dependent_pairFormation_alt lambdaEquality_alt dependent_set_memberEquality_alt approximateComputation universeIsType productIsType imageElimination functionIsType functionExtensionality inhabitedIsType equalityIstype

Latex:
\mforall{}[T:Type].  \mforall{}L1,L:T  List.    (interleaving(T;[];L1;L)  \mLeftarrow{}{}\mRightarrow{}  L  =  L1)

Date html generated: 2020_05_20-AM-07_48_18
Last ObjectModification: 2020_01_07-PM-02_28_50

Theory : list!

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