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: all: x:A. B[x] implies:  Q natural_number: $n
Definitions unfolded in proof :  all: x:A. B[x] implies:  Q member: t ∈ T uall: [x:A]. B[x] prop: uimplies: supposing a itermConstant: "const" req_int_terms: t1 ≡ t2 top: Top uiff: uiff(P;Q) and: P ∧ Q false: False not: ¬A iff: ⇐⇒ 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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