Nuprl Lemma : iseg_ge_length

[T:Type]. ∀[L1,L2:T List].  (L1 L2 ∈ (T List)) supposing ((||L1|| ≥ ||L2|| and L1 ≤ L2)


Definitions occuring in Statement :  iseg: l1 ≤ l2 length: ||as|| list: List uimplies: supposing a uall: [x:A]. B[x] ge: i ≥  universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a prop: ge: i ≥  all: x:A. B[x] decidable: Dec(P) or: P ∨ Q le: A ≤ B and: P ∧ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False implies:  Q not: ¬A top: Top
Lemmas referenced :  int_formula_prop_wf int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformle_wf itermVar_wf intformeq_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__equal_int iseg_same_length list_wf iseg_wf length_wf ge_wf iseg_length
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination hypothesis sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry universeEquality dependent_functionElimination unionElimination productElimination natural_numberEquality dependent_pairFormation lambdaEquality int_eqEquality intEquality voidElimination voidEquality independent_pairFormation computeAll

\mforall{}[T:Type].  \mforall{}[L1,L2:T  List].    (L1  =  L2)  supposing  ((||L1||  \mgeq{}  ||L2||  )  and  L1  \mleq{}  L2)

Date html generated: 2016_05_14-PM-01_34_53
Last ObjectModification: 2016_01_15-AM-08_25_47

Theory : list_1

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