### Nuprl Lemma : length_interleaving

`∀[T:Type]. ∀[L,L1,L2:T List].  ||L|| = (||L1|| + ||L2||) ∈ ℕ supposing interleaving(T;L1;L2;L)`

Proof

Definitions occuring in Statement :  interleaving: `interleaving(T;L1;L2;L)` length: `||as||` list: `T List` nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` add: `n + m` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  interleaving: `interleaving(T;L1;L2;L)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` and: `P ∧ Q` prop: `ℙ` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` guard: `{T}` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` false: `False` uiff: `uiff(P;Q)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top`
Lemmas referenced :  equal_wf nat_wf length_wf_nat length_wf add_nat_wf nat_properties decidable__le add-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf itermAdd_wf intformeq_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_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_wf false_wf le_wf disjoint_sublists_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin hypothesis productEquality extract_by_obid isectElimination cumulativity hypothesisEquality dependent_set_memberEquality addEquality lambdaFormation equalityTransitivity equalitySymmetry applyLambdaEquality setElimination rename dependent_functionElimination natural_numberEquality unionElimination pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination because_Cache axiomEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L,L1,L2:T  List].    ||L||  =  (||L1||  +  ||L2||)  supposing  interleaving(T;L1;L2;L)

Date html generated: 2017_10_01-AM-08_36_13
Last ObjectModification: 2017_07_26-PM-04_26_07

Theory : list!

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