Nuprl Lemma : radd-rmin

[x,y,z:ℝ].  ((x rmin(y;z)) rmin(x y;x z))


Proof




Definitions occuring in Statement :  rmin: rmin(x;y) req: y radd: b real: uall: [x:A]. B[x]
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a implies:  Q subtype_rel: A ⊆B real: rmin: rmin(x;y) all: x:A. B[x] iff: ⇐⇒ Q rev_implies:  Q true: True bool: 𝔹 unit: Unit it: btrue: tt ifthenelse: if then else fi  le: A ≤ B bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b false: False not: ¬A nat_plus: + satisfiable_int_formula: satisfiable_int_formula(fmla) top: Top squash: T
Lemmas referenced :  req-iff-bdd-diff radd_wf rmin_wf req_witness real_wf nat_plus_wf imin_wf trivial-bdd-diff bdd-diff_functionality radd-bdd-diff rmin_functionality_wrt_bdd-diff ifthenelse_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf nat_plus_properties less_than_wf satisfiable-full-omega-tt intformand_wf intformle_wf itermVar_wf intformnot_wf itermAdd_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_term_value_add_lemma int_formula_prop_wf add-is-int-iff false_wf squash_wf true_wf add_functionality_wrt_eq imin_unfold iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis productElimination independent_isectElimination independent_functionElimination sqequalRule isect_memberEquality because_Cache applyEquality lambdaEquality setElimination rename addEquality lambdaFormation dependent_functionElimination intEquality natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp instantiate cumulativity voidElimination dependent_set_memberEquality int_eqEquality voidEquality independent_pairFormation computeAll pointwiseFunctionality baseApply closedConclusion baseClosed imageElimination universeEquality imageMemberEquality

Latex:
\mforall{}[x,y,z:\mBbbR{}].    ((x  +  rmin(y;z))  =  rmin(x  +  y;x  +  z))



Date html generated: 2017_10_03-AM-08_29_12
Last ObjectModification: 2017_07_28-AM-07_25_45

Theory : reals


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