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
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