### Nuprl Lemma : rmin-int

`∀[a,b:ℤ].  (rmin(r(a);r(b)) = r(imin(a;b)))`

Proof

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

Latex:
\mforall{}[a,b:\mBbbZ{}].    (rmin(r(a);r(b))  =  r(imin(a;b)))

Date html generated: 2017_10_03-AM-08_28_51
Last ObjectModification: 2017_07_28-AM-07_25_32

Theory : reals

Home Index