`∀[a,b,c:ℤ].  ((imax(a;b) + c) = imax(a + c;b + c) ∈ ℤ)`

Proof

Definitions occuring in Statement :  imax: `imax(a;b)` uall: `∀[x:A]. B[x]` add: `n + m` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  imax: `imax(a;b)` uall: `∀[x:A]. B[x]` member: `t ∈ T` has-value: `(a)↓` uimplies: `b supposing a` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` ifthenelse: `if b then t else f fi ` 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` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  value-type-has-value int-value-type 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 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
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut callbyvalueReduce extract_by_obid sqequalHypSubstitution isectElimination thin because_Cache independent_isectElimination hypothesis addEquality hypothesisEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination natural_numberEquality lambdaEquality int_eqEquality intEquality isect_memberEquality voidEquality independent_pairFormation computeAll axiomEquality

Latex:
\mforall{}[a,b,c:\mBbbZ{}].    ((imax(a;b)  +  c)  =  imax(a  +  c;b  +  c))

Date html generated: 2017_04_14-AM-09_14_20
Last ObjectModification: 2017_02_27-PM-03_51_40

Theory : int_2

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