Nuprl Lemma : reg_seq_mul_wf
∀[x,y:ℕ+ ⟶ ℤ]. (reg_seq_mul(x;y) ∈ ℕ+ ⟶ ℤ)
Proof
Definitions occuring in Statement :
reg_seq_mul: reg_seq_mul(x;y),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
reg_seq_mul: reg_seq_mul(x;y),
nat_plus: ℕ+,
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 :
rounding-div_wf,
nat_plus_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-less_than,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
multiplyEquality,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality_alt,
natural_numberEquality,
setElimination,
rename,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isectIsTypeImplies,
functionIsType
Latex:
\mforall{}[x,y:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. (reg\_seq\_mul(x;y) \mmember{} \mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{})
Date html generated:
2019_10_16-PM-03_06_05
Last ObjectModification:
2019_02_15-AM-10_14_30
Theory : reals
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