### Nuprl Lemma : pointwise-rleq_wf

`∀[n,m:ℤ]. ∀[x,y:{n..m + 1-} ⟶ ℝ].  (x[k] ≤ y[k] for k ∈ [n,m] ∈ ℙ)`

Proof

Definitions occuring in Statement :  pointwise-rleq: `x[k] ≤ y[k] for k ∈ [n,m]` real: `ℝ` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  pointwise-rleq: `x[k] ≤ y[k] for k ∈ [n,m]` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top`
Lemmas referenced :  real_wf int_seg_wf lelt_wf int_formula_prop_wf int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformle_wf itermConstant_wf itermAdd_wf itermVar_wf intformless_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__lt rleq_wf le_wf all_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin intEquality lambdaEquality functionEquality hypothesisEquality hypothesis because_Cache applyEquality dependent_set_memberEquality independent_pairFormation dependent_functionElimination addEquality natural_numberEquality unionElimination independent_isectElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll axiomEquality equalityTransitivity equalitySymmetry

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

Date html generated: 2016_05_18-AM-07_44_39
Last ObjectModification: 2016_01_17-AM-02_06_16

Theory : reals

Home Index