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: List nat: uimplies: supposing a uall: [x:A]. B[x] add: m universe: Type equal: t ∈ T
Definitions unfolded in proof :  interleaving: interleaving(T;L1;L2;L) uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a and: P ∧ Q prop: nat: all: x:A. B[x] implies:  Q guard: {T} ge: i ≥  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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