### Nuprl Lemma : rmaximum_wf

`∀[n,m:ℤ].  ∀[x:{n..m + 1-} ⟶ ℝ]. (rmaximum(n;m;k.x[k]) ∈ ℝ) supposing n ≤ m`

Proof

Definitions occuring in Statement :  rmaximum: `rmaximum(n;m;k.x[k])` real: `ℝ` int_seg: `{i..j-}` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s]` le: `A ≤ B` member: `t ∈ T` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  rmaximum: `rmaximum(n;m;k.x[k])` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` nat: `ℕ` 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` implies: `P `` Q` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` so_apply: `x[s]` int_seg: `{i..j-}` lelt: `i ≤ j < k` guard: `{T}`
Lemmas referenced :  int_seg_wf int_seg_properties rmax_wf lelt_wf int_term_value_add_lemma int_formula_prop_less_lemma itermAdd_wf intformless_wf decidable__lt le_wf int_formula_prop_wf int_term_value_var_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermSubtract_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt subtract_wf decidable__le real_wf primrec_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis dependent_set_memberEquality because_Cache dependent_functionElimination natural_numberEquality hypothesisEquality unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll applyEquality addEquality setElimination rename productElimination axiomEquality equalityTransitivity equalitySymmetry functionEquality

Latex:
\mforall{}[n,m:\mBbbZ{}].    \mforall{}[x:\{n..m  +  1\msupminus{}\}  {}\mrightarrow{}  \mBbbR{}].  (rmaximum(n;m;k.x[k])  \mmember{}  \mBbbR{})  supposing  n  \mleq{}  m

Date html generated: 2016_05_18-AM-07_49_48
Last ObjectModification: 2016_01_17-AM-02_09_04

Theory : reals

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