Nuprl Lemma : interleaving_of_nil

`∀[T:Type]. ∀L1,L2:T List.  (interleaving(T;L1;L2;[]) `⇐⇒` (L1 = [] ∈ (T List)) ∧ (L2 = [] ∈ (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` and: `P ∧ Q` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` member: `t ∈ T` uiff: `uiff(P;Q)` uimplies: `b supposing a` ge: `i ≥ j ` nat: `ℕ` guard: `{T}` 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]` top: `Top` prop: `ℙ` rev_implies: `P `` Q`
Lemmas referenced :  length_zero length_interleaving nil_wf length_of_nil_lemma non_neg_length nat_properties decidable__equal_int length_wf full-omega-unsat intformand_wf intformnot_wf intformeq_wf itermVar_wf itermConstant_wf intformle_wf itermAdd_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_term_value_add_lemma int_formula_prop_wf interleaving_wf equal-wf-T-base list_wf nil_interleaving
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt lambdaFormation independent_pairFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality productElimination independent_isectElimination because_Cache hypothesis sqequalRule equalityTransitivity equalitySymmetry applyLambdaEquality setElimination rename dependent_functionElimination unionElimination natural_numberEquality approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality productEquality baseClosed universeIsType universeEquality hyp_replacement

Latex:
\mforall{}[T:Type].  \mforall{}L1,L2:T  List.    (interleaving(T;L1;L2;[])  \mLeftarrow{}{}\mRightarrow{}  (L1  =  [])  \mwedge{}  (L2  =  []))

Date html generated: 2019_10_15-AM-10_55_38
Last ObjectModification: 2018_09_27-AM-10_42_47

Theory : list!

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