Nuprl Lemma : fund-theorem-arithmetic
Bij(ℕ+;bag(Prime);λn.factors(n))
Proof
Definitions occuring in Statement :
factors: factors(n),
Prime: Prime,
bag: bag(T),
biject: Bij(A;B;f),
nat_plus: ℕ+,
lambda: λx.A[x]
Definitions unfolded in proof :
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
surject: Surj(A;B;f),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
Prime: Prime,
int_upper: {i...},
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
bag_wf,
Prime_wf,
factors_wf,
nat_plus_wf,
int-bag-product_wf,
subtype_rel_bag,
squash_wf,
true_wf,
product-factors,
iff_weakening_equal,
nat_plus_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
itermConstant_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
less_than_wf,
bag-product-primes,
factors-prime-product
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaFormation,
sqequalRule,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyLambdaEquality,
applyEquality,
intEquality,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
because_Cache,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality
Latex:
Bij(\mBbbN{}\msupplus{};bag(Prime);\mlambda{}n.factors(n))
Date html generated:
2018_05_21-PM-07_23_19
Last ObjectModification:
2017_07_26-PM-05_06_15
Theory : general
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