Nuprl Lemma : select_equal

[T:Type]. ∀[a,b:T List]. ∀[i:ℕ].  (a[i] b[i] ∈ T) supposing (i < ||a|| and (a b ∈ (T List)))


Definitions occuring in Statement :  select: L[n] length: ||as|| list: List nat: less_than: a < b uimplies: supposing a uall: [x:A]. B[x] universe: Type equal: t ∈ T
Definitions unfolded in proof :  member: t ∈ T uall: [x:A]. B[x] nat: uimplies: supposing a prop: implies:  Q ge: i ≥  all: x:A. B[x] decidable: Dec(P) or: P ∨ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A top: Top and: P ∧ Q
Lemmas referenced :  less_than_wf length_wf equal_wf list_wf nat_wf select_wf nat_properties decidable__le satisfiable-full-omega-tt 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
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis cumulativity because_Cache universeEquality isect_memberFormation sqequalRule isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry hyp_replacement applyLambdaEquality lambdaFormation independent_isectElimination dependent_functionElimination natural_numberEquality unionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality voidElimination voidEquality independent_pairFormation computeAll functionEquality independent_functionElimination

\mforall{}[T:Type].  \mforall{}[a,b:T  List].  \mforall{}[i:\mBbbN{}].    (a[i]  =  b[i])  supposing  (i  <  ||a||  and  (a  =  b))

Date html generated: 2017_04_17-AM-08_42_56
Last ObjectModification: 2017_02_27-PM-05_01_50

Theory : list_1

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