Nuprl Lemma : bool-cardinality-le

|š”¹| ā‰¤ 2


Proof




Definitions occuring in Statement :  cardinality-le: |T| ā‰¤ n bool: š”¹ natural_number: $n
Definitions unfolded in proof :  uall: āˆ€[x:A]. B[x] member: t āˆˆ T all: āˆ€x:A. B[x] implies: ā‡’ Q length: ||as|| list_ind: list_ind cons: [a b] nil: [] it: ā‹… bool: š”¹ unit: Unit btrue: tt uiff: uiff(P;Q) and: P āˆ§ Q uimplies: supposing a l_member: (x āˆˆ l) exists: āˆƒx:A. B[x] nat: ā„• le: A ā‰¤ B less_than': less_than'(a;b) not: Ā¬A false: False select: L[n] cand: cāˆ§ B less_than: a < b squash: ā†“T true: True ge: i ā‰„  decidable: Dec(P) or: P āˆØ Q satisfiable_int_formula: satisfiable_int_formula(fmla) prop: ā„™ bfalse: ff sq_type: SQType(T) guard: {T} bnot: Ā¬bb ifthenelse: if then else fi  assert: ā†‘b subtract: m
Lemmas referenced :  list-cardinality-le bool_wf cons_wf btrue_wf bfalse_wf nil_wf eqtt_to_assert istype-void istype-le length_of_cons_lemma length_of_nil_lemma istype-less_than length_wf select_wf nat_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf istype-int 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 eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot
Rules used in proof :  cut introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesis dependent_functionElimination independent_functionElimination sqequalRule lambdaFormation_alt hypothesisEquality inhabitedIsType unionElimination equalityElimination productElimination independent_isectElimination dependent_pairFormation_alt dependent_set_memberEquality_alt natural_numberEquality independent_pairFormation voidElimination Error :memTop,  imageMemberEquality baseClosed productIsType setElimination rename equalityIstype because_Cache approximateComputation lambdaEquality_alt int_eqEquality universeIsType sqequalBase equalitySymmetry equalityTransitivity promote_hyp instantiate cumulativity

Latex:
|\mBbbB{}|  \mleq{}  2



Date html generated: 2020_05_19-PM-09_43_31
Last ObjectModification: 2019_12_31-PM-00_28_25

Theory : list_1


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