Nuprl Lemma : frs-mesh-nonneg

`∀[p:ℝ List]. (frs-non-dec(p) `` (r0 ≤ frs-mesh(p)))`

Proof

Definitions occuring in Statement :  frs-mesh: `frs-mesh(p)` frs-non-dec: `frs-non-dec(L)` rleq: `x ≤ y` int-to-real: `r(n)` real: `ℝ` list: `T List` uall: `∀[x:A]. B[x]` implies: `P `` Q` natural_number: `\$n`
Definitions unfolded in proof :  frs-mesh: `frs-mesh(p)` uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` all: `∀x:A. B[x]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` rleq: `x ≤ y` rnonneg: `rnonneg(x)` le: `A ≤ B` nat_plus: `ℕ+` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` so_lambda: `λ2x.t[x]` int_seg: `{i..j-}` lelt: `i ≤ j < k` less_than: `a < b` squash: `↓T` so_apply: `x[s]` subtype_rel: `A ⊆r B` less_than': `less_than'(a;b)` rev_uimplies: `rev_uimplies(P;Q)` rge: `x ≥ y` frs-non-dec: `frs-non-dec(L)` itermConstant: `"const"` req_int_terms: `t1 ≡ t2`
Lemmas referenced :  lt_int_wf length_wf real_wf bool_wf eqtt_to_assert assert_of_lt_int rleq_weakening_equal int-to-real_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot less_than_wf frs-non-dec_wf less_than'_wf rsub_wf rmaximum_wf subtract_wf nat_plus_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf select_wf int_seg_properties itermAdd_wf int_term_value_add_lemma decidable__lt add-is-int-iff subtract-is-int-iff false_wf int_seg_wf nat_plus_wf list_wf rmaximum_ub rleq_functionality_wrt_implies radd-preserves-rleq radd_wf lelt_wf rleq_functionality real_term_polynomial real_term_value_const_lemma real_term_value_sub_lemma real_term_value_add_lemma real_term_value_var_lemma req-iff-rsub-is-0
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis hypothesisEquality natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache dependent_pairFormation promote_hyp dependent_functionElimination instantiate independent_functionElimination voidElimination lambdaEquality independent_pairEquality applyEquality cumulativity setElimination rename int_eqEquality intEquality isect_memberEquality voidEquality independent_pairFormation computeAll addEquality pointwiseFunctionality imageElimination baseApply closedConclusion baseClosed minusEquality axiomEquality dependent_set_memberEquality

Latex:
\mforall{}[p:\mBbbR{}  List].  (frs-non-dec(p)  {}\mRightarrow{}  (r0  \mleq{}  frs-mesh(p)))

Date html generated: 2017_10_03-AM-09_36_07
Last ObjectModification: 2017_07_28-AM-07_53_51

Theory : reals

Home Index