Nuprl Lemma : imin_nat_plus

[a,b:ℕ+].  (imin(a;b) ∈ ℕ+)


Proof




Definitions occuring in Statement :  imin: imin(a;b) nat_plus: + uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T nat_plus: + squash: T prop: true: True subtype_rel: A ⊆B uimplies: supposing a guard: {T} iff: ⇐⇒ Q and: P ∧ Q rev_implies:  Q implies:  Q all: x:A. B[x] bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) ifthenelse: if then else fi  decidable: Dec(P) or: P ∨ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A top: Top bfalse: ff sq_type: SQType(T) bnot: ¬bb assert: b
Lemmas referenced :  imin_wf less_than_wf squash_wf true_wf imin_unfold iff_weakening_equal le_int_wf bool_wf eqtt_to_assert assert_of_le_int nat_plus_properties decidable__lt satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf nat_plus_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut dependent_set_memberEquality extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename because_Cache hypothesis applyEquality lambdaEquality imageElimination hypothesisEquality equalityTransitivity equalitySymmetry intEquality natural_numberEquality sqequalRule imageMemberEquality baseClosed universeEquality independent_isectElimination productElimination independent_functionElimination lambdaFormation unionElimination equalityElimination dependent_functionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll promote_hyp instantiate cumulativity axiomEquality

Latex:
\mforall{}[a,b:\mBbbN{}\msupplus{}].    (imin(a;b)  \mmember{}  \mBbbN{}\msupplus{})



Date html generated: 2017_04_14-AM-09_14_01
Last ObjectModification: 2017_02_27-PM-03_51_28

Theory : int_2


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