Nuprl Lemma : pointwise-req_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-req: x[k] y[k] for k ∈ [n,m] real: int_seg: {i..j-} uall: [x:A]. B[x] prop: so_apply: x[s] member: t ∈ T function: x:A ⟶ B[x] add: m natural_number: $n int:
Definitions unfolded in proof :  pointwise-req: x[k] y[k] for k ∈ [n,m] uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] implies:  Q prop: 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: 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 req_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]  =  y[k]  for  k  \mmember{}  [n,m]  \mmember{}  \mBbbP{})



Date html generated: 2016_05_18-AM-07_44_28
Last ObjectModification: 2016_01_17-AM-02_07_01

Theory : reals


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