Nuprl Lemma : bpa-mul_wf
∀[p:ℕ+]. ∀[x,y:basic-padic(p)]. (bpa-mul(p;x;y) ∈ basic-padic(p))
Proof
Definitions occuring in Statement :
bpa-mul: bpa-mul(p;x;y),
basic-padic: basic-padic(p),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bpa-mul: bpa-mul(p;x;y),
basic-padic: basic-padic(p),
nat: ℕ,
nat_plus: ℕ+,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
nat_properties,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
p-mul_wf,
basic-padic_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
because_Cache,
hypothesis,
extract_by_obid,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[x,y:basic-padic(p)]. (bpa-mul(p;x;y) \mmember{} basic-padic(p))
Date html generated:
2018_05_21-PM-03_23_46
Last ObjectModification:
2018_05_19-AM-08_22_05
Theory : rings_1
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