`∀[x,y,z:ℝ].  ((x + rmax(y;z)) = rmax(x + y;x + z))`

Proof

Definitions occuring in Statement :  rmax: `rmax(x;y)` req: `x = y` radd: `a + b` real: `ℝ` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` implies: `P `` Q` subtype_rel: `A ⊆r B` real: `ℝ` rmax: `rmax(x;y)` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` true: `True` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` le: `A ≤ B` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` nat_plus: `ℕ+` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` squash: `↓T`
Lemmas referenced :  req-iff-bdd-diff radd_wf rmax_wf req_witness real_wf nat_plus_wf imax_wf bdd-diff_functionality radd-bdd-diff rmax_functionality_wrt_bdd-diff trivial-bdd-diff ifthenelse_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf nat_plus_properties less_than_wf satisfiable-full-omega-tt intformand_wf intformle_wf itermVar_wf intformnot_wf itermAdd_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_term_value_add_lemma int_formula_prop_wf add-is-int-iff false_wf squash_wf true_wf add_functionality_wrt_eq 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 productElimination independent_isectElimination independent_functionElimination sqequalRule isect_memberEquality because_Cache applyEquality lambdaEquality setElimination rename addEquality dependent_functionElimination lambdaFormation intEquality natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp instantiate cumulativity voidElimination dependent_set_memberEquality int_eqEquality voidEquality independent_pairFormation computeAll pointwiseFunctionality baseApply closedConclusion baseClosed imageElimination universeEquality imageMemberEquality

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

Date html generated: 2017_10_03-AM-08_28_38
Last ObjectModification: 2017_07_28-AM-07_25_23

Theory : reals

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