Nuprl Lemma : posint_reduc_dec
∀a:|<ℤ+,*>|. Dec(Reducible(a))
Proof
Definitions occuring in Statement :
posint_mul_mon: <ℤ+,*>,
mreducible: Reducible(a),
decidable: Dec(P),
all: ∀x:A. B[x],
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
mpdivides: a p| b,
mdivides: b | a,
posint_mul_mon: <ℤ+,*>,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
exists: ∃x:A. B[x],
nat_plus: ℕ+,
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
uiff: uiff(P;Q),
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
cand: A c∧ B
Lemmas referenced :
decidable_functionality,
mreducible_wf,
posint_mul_mon_wf,
mon_subtype_grp_sig,
abmonoid_subtype_mon,
subtype_rel_transitivity,
abmonoid_wf,
mon_wf,
grp_sig_wf,
exists_wf,
grp_car_wf,
not_wf,
munit_wf,
mpdivides_wf,
mreducible_elim,
abmonoid_subtype_iabmonoid,
posint_cancel,
nat_plus_wf,
equal_wf,
mul_nat_plus,
equal-wf-T-base,
divides_wf,
posint_munit_elim,
istype-int,
set_subtype_base,
less_than_wf,
int_subtype_base,
divides_nchar,
pdivisor_bound,
nat_plus_subtype_nat,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformless_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
equal-wf-base,
decidable__lt,
istype-false,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
int_seg_properties,
lelt_wf,
int_seg_wf,
decidable__exists_int_seg,
decidable__divides_ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesis,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
hypothesisEquality,
because_Cache,
lambdaEquality_alt,
productEquality,
inhabitedIsType,
independent_functionElimination,
productElimination,
universeIsType,
setElimination,
rename,
independent_pairFormation,
dependent_pairFormation_alt,
equalityIsType4,
baseApply,
closedConclusion,
baseClosed,
intEquality,
natural_numberEquality,
promote_hyp,
productIsType,
equalityIsType3,
multiplyEquality,
dependent_set_memberEquality_alt,
unionElimination,
approximateComputation,
int_eqEquality,
isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}a:|<\mBbbZ{}\msupplus{},*>|. Dec(Reducible(a))
Date html generated:
2019_10_16-PM-01_06_08
Last ObjectModification:
2018_10_08-PM-00_18_42
Theory : factor_1
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