### Nuprl Lemma : rmax-req

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

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` rmax: `rmax(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` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` rev_implies: `P `` Q` exists: `∃x:A. B[x]` nat_plus: `ℕ+` prop: `ℙ` so_lambda: `λ2x.t[x]` int_upper: `{i...}` real: `ℝ` le: `A ≤ B` guard: `{T}` subtype_rel: `A ⊆r B` so_apply: `x[s]` rmax: `rmax(x;y)` true: `True` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` top: `Top` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` squash: `↓T`
Lemmas referenced :  rleq_antisymmetry rmax_wf rleq-iff int_upper_wf all_wf le_wf subtract_wf less_than_transitivity1 less_than_wf nat_plus_wf rleq-rmax req_witness rleq_wf real_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int int_upper_properties nat_plus_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermMultiply_wf itermConstant_wf itermVar_wf itermSubtract_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_mul_lemma int_term_value_constant_lemma int_term_value_var_lemma int_term_value_subtract_lemma int_formula_prop_less_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot squash_wf true_wf imax_unfold iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis independent_isectElimination dependent_functionElimination because_Cache productElimination independent_functionElimination lambdaFormation dependent_pairFormation setElimination rename sqequalRule lambdaEquality multiplyEquality minusEquality natural_numberEquality applyEquality dependent_set_memberEquality isect_memberEquality equalityTransitivity equalitySymmetry unionElimination equalityElimination int_eqEquality intEquality voidElimination voidEquality independent_pairFormation computeAll promote_hyp instantiate cumulativity imageElimination imageMemberEquality baseClosed universeEquality

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

Date html generated: 2017_10_03-AM-08_30_05
Last ObjectModification: 2017_07_28-AM-07_26_20

Theory : reals

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