Nuprl Lemma : not-rless

[x,y:ℝ].  y ≤ supposing ¬(x < y)


Proof




Definitions occuring in Statement :  rleq: x ≤ y rless: x < y real: uimplies: supposing a uall: [x:A]. B[x] not: ¬A
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a iff: ⇐⇒ Q and: P ∧ Q rev_implies:  Q implies:  Q all: x:A. B[x] real: decidable: Dec(P) or: P ∨ Q not: ¬A rless: x < y sq_exists: x:{A| B[x]} nat_plus: + prop: satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False top: Top rleq: x ≤ y rnonneg: rnonneg(x) le: A ≤ B subtype_rel: A ⊆B
Lemmas referenced :  rless_wf not_wf real_wf rsub_wf less_than'_wf nat_plus_wf int_formula_prop_wf int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_term_value_add_lemma int_formula_prop_less_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformle_wf itermConstant_wf itermVar_wf itermAdd_wf intformless_wf intformnot_wf intformand_wf satisfiable-full-omega-tt less_than_wf decidable__lt nat_plus_properties decidable__le rleq-iff4
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality productElimination independent_functionElimination lambdaFormation dependent_functionElimination applyEquality setElimination rename addEquality natural_numberEquality hypothesis unionElimination dependent_set_memberFormation dependent_set_memberEquality because_Cache independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_pairEquality minusEquality axiomEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[x,y:\mBbbR{}].    y  \mleq{}  x  supposing  \mneg{}(x  <  y)



Date html generated: 2016_05_18-AM-07_13_07
Last ObjectModification: 2016_01_17-AM-01_52_12

Theory : reals


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