### Nuprl Lemma : rleq_antisymmetry

`∀[x,y:ℝ].  (x = y) supposing ((y ≤ x) and (x ≤ y))`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` req: `x = y` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` req: `x = y` all: `∀x:A. B[x]` prop: `ℙ` real: `ℝ` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` nat_plus: `ℕ+` 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`
Lemmas referenced :  rleq-iff4 nat_plus_wf req_witness rleq_wf real_wf absval_unfold subtract_wf 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 itermSubtract_wf itermVar_wf itermConstant_wf itermAdd_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_term_value_constant_lemma int_term_value_add_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot itermMinus_wf int_term_value_minus_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis productElimination independent_functionElimination lambdaFormation dependent_functionElimination because_Cache sqequalRule isect_memberEquality equalityTransitivity equalitySymmetry applyEquality setElimination rename minusEquality natural_numberEquality unionElimination equalityElimination independent_isectElimination lessCases sqequalAxiom independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality computeAll promote_hyp instantiate cumulativity

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

Date html generated: 2017_10_03-AM-08_25_03
Last ObjectModification: 2017_07_28-AM-07_23_40

Theory : reals

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