### Nuprl Lemma : rminus-nonneg

`∀[x:ℝ]. (x = r0) supposing (rnonneg(-(x)) and rnonneg(x))`

Proof

Definitions occuring in Statement :  rnonneg: `rnonneg(x)` req: `x = y` rminus: `-(x)` int-to-real: `r(n)` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` rminus: `-(x)` rnonneg: `rnonneg(x)` req: `x = y` all: `∀x:A. B[x]` int-to-real: `r(n)` implies: `P `` Q` prop: `ℙ` subtype_rel: `A ⊆r B` real: `ℝ` nat_plus: `ℕ+` top: `Top` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` less_than: `a < b` less_than': `less_than'(a;b)` true: `True` squash: `↓T` not: `¬A` false: `False` le: `A ≤ B` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` subtract: `n - m`
Lemmas referenced :  nat_plus_wf req_witness int-to-real_wf rnonneg_wf rminus_wf real_wf absval_unfold lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf nat_plus_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermVar_wf itermConstant_wf itermMinus_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_term_value_constant_lemma int_term_value_minus_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot minus-one-mul mul-associates mul-commutes zero-mul add-zero
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution sqequalRule lambdaFormation extract_by_obid hypothesis isectElimination thin hypothesisEquality natural_numberEquality independent_functionElimination applyEquality lambdaEquality setElimination rename isect_memberEquality because_Cache equalityTransitivity equalitySymmetry multiplyEquality voidElimination voidEquality dependent_functionElimination minusEquality unionElimination equalityElimination productElimination independent_isectElimination lessCases sqequalAxiom independent_pairFormation imageMemberEquality baseClosed imageElimination dependent_set_memberEquality dependent_pairFormation int_eqEquality intEquality computeAll promote_hyp instantiate cumulativity

Latex:
\mforall{}[x:\mBbbR{}].  (x  =  r0)  supposing  (rnonneg(-(x))  and  rnonneg(x))

Date html generated: 2017_10_03-AM-08_24_15
Last ObjectModification: 2017_07_28-AM-07_23_13

Theory : reals

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