### Nuprl Lemma : rinv-negative

`∀x:ℝ. ((x < r0) `` (rinv(x) < r0))`

Proof

Definitions occuring in Statement :  rless: `x < y` rinv: `rinv(x)` int-to-real: `r(n)` real: `ℝ` all: `∀x:A. B[x]` implies: `P `` Q` natural_number: `\$n`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` uall: `∀[x:A]. B[x]` prop: `ℙ` uimplies: `b supposing a` itermConstant: `"const"` req_int_terms: `t1 ≡ t2` top: `Top` uiff: `uiff(P;Q)` and: `P ∧ Q` false: `False` not: `¬A` iff: `P `⇐⇒` Q` rneq: `x ≠ y` guard: `{T}` or: `P ∨ Q`
Lemmas referenced :  rminus-reverses-rless int-to-real_wf rless_wf real_wf rminus_wf rmul_wf rless_functionality real_term_polynomial itermSubtract_wf itermMinus_wf itermConstant_wf real_term_value_const_lemma real_term_value_sub_lemma real_term_value_minus_lemma req-iff-rsub-is-0 req_transitivity itermVar_wf itermMultiply_wf real_term_value_var_lemma real_term_value_mul_lemma req_inversion rminus-as-rmul rinv-positive rinv_wf2 req_weakening rinv-rminus rless-implies-rless rsub_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality isectElimination natural_numberEquality hypothesis independent_functionElimination because_Cache minusEquality independent_isectElimination sqequalRule computeAll lambdaEquality intEquality isect_memberEquality voidElimination voidEquality productElimination int_eqEquality inrFormation inlFormation

Latex:
\mforall{}x:\mBbbR{}.  ((x  <  r0)  {}\mRightarrow{}  (rinv(x)  <  r0))

Date html generated: 2017_10_03-AM-08_28_04
Last ObjectModification: 2017_07_28-AM-07_25_00

Theory : reals

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