### Nuprl Lemma : reg-seq-mul-comm

`∀[x,y:ℕ+ ⟶ ℤ].  (reg-seq-mul(x;y) = reg-seq-mul(y;x) ∈ (ℕ+ ⟶ ℤ))`

Proof

Definitions occuring in Statement :  reg-seq-mul: `reg-seq-mul(x;y)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` reg-seq-mul: `reg-seq-mul(x;y)` subtype_rel: `A ⊆r B` top: `Top` nat_plus: `ℕ+` nequal: `a ≠ b ∈ T ` not: `¬A` implies: `P `` Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` all: `∀x:A. B[x]` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  nat_plus_wf equal_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_formula_prop_eq_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf itermMultiply_wf intformeq_wf intformand_wf satisfiable-full-omega-tt nat_plus_properties mul-commutes
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaEquality sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality hypothesis isect_memberEquality voidElimination voidEquality intEquality divideEquality multiplyEquality because_Cache natural_numberEquality setElimination rename lambdaFormation independent_isectElimination dependent_pairFormation int_eqEquality dependent_functionElimination independent_pairFormation computeAll axiomEquality

Latex:
\mforall{}[x,y:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}].    (reg-seq-mul(x;y)  =  reg-seq-mul(y;x))

Date html generated: 2016_05_18-AM-06_49_32
Last ObjectModification: 2016_01_17-AM-01_45_44

Theory : reals

Home Index