### Nuprl Lemma : nil_interleaving2

`∀[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 :  interleaving: `interleaving(T;L1;L2;L)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` member: `t ∈ T` subtype_rel: `A ⊆r B` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` prop: `ℙ` rev_implies: `P `` Q` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` false: `False` le: `A ≤ B` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` squash: `↓T` true: `True` guard: `{T}` uiff: `uiff(P;Q)` 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` less_than': `less_than'(a;b)`
Lemmas referenced :  length_of_nil_lemma istype-nat length_wf_nat set_subtype_base le_wf istype-int int_subtype_base length_wf disjoint_sublists_wf nil_wf non_neg_length 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 equal_wf squash_wf true_wf istype-universe list_wf subtype_rel_self iff_weakening_equal add-zero istype-le disjoint_sublists_sublist proper_sublist_length nat_properties decidable__equal_int add-is-int-iff intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma false_wf stuck-spread istype-base int_seg_wf int_seg_properties decidable__lt intformless_wf int_formula_prop_less_lemma istype-less_than id_increasing select_wf istype-void increasing_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep cut introduction extract_by_obid hypothesis isect_memberFormation_alt lambdaFormation_alt independent_pairFormation sqequalHypSubstitution productElimination thin productIsType equalityIstype isectElimination hypothesisEquality applyEquality intEquality lambdaEquality_alt natural_numberEquality independent_isectElimination addEquality sqequalBase equalitySymmetry universeIsType dependent_functionElimination because_Cache unionElimination approximateComputation independent_functionElimination dependent_pairFormation_alt int_eqEquality Error :memTop,  voidElimination dependent_set_memberEquality_alt imageElimination equalityTransitivity instantiate universeEquality imageMemberEquality baseClosed inhabitedIsType applyLambdaEquality setElimination rename pointwiseFunctionality promote_hyp baseApply closedConclusion functionIsType functionExtensionality hyp_replacement

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_20
Last ObjectModification: 2020_01_22-PM-03_32_07

Theory : list!

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