Nuprl Lemma : strong_before_wf

[T:Type]. ∀[L:T List]. ∀[x,y:T].  (x << y ∈ L ∈ ℙ)


Proof




Definitions occuring in Statement :  strong_before: x << y ∈ l list: List uall: [x:A]. B[x] prop: member: t ∈ T universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T strong_before: x << y ∈ l prop: and: P ∧ Q so_lambda: λ2x.t[x] implies:  Q nat: uimplies: supposing a 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 so_apply: x[s]
Lemmas referenced :  l_member_wf all_wf nat_wf less_than_wf length_wf equal_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 list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule productEquality extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis because_Cache lambdaEquality functionEquality setElimination rename independent_isectElimination productElimination dependent_functionElimination natural_numberEquality unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll axiomEquality equalityTransitivity equalitySymmetry universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[x,y:T].    (x  <<  y  \mmember{}  L  \mmember{}  \mBbbP{})



Date html generated: 2017_10_01-AM-08_33_45
Last ObjectModification: 2017_07_26-PM-04_25_16

Theory : list!


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