Nuprl Lemma : posint_unit_dec
∀a:|<ℤ+,*>|. Dec(<ℤ+,*>-unit(a))
Proof
Definitions occuring in Statement :
posint_mul_mon: <ℤ+,*>,
munit: g-unit(u),
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,
abmonoid: AbMon,
mon: Mon,
posint_mul_mon: <ℤ+,*>,
grp_car: |g|,
pi1: fst(t),
nat_plus: ℕ+,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
decidable_functionality,
munit_wf,
posint_mul_mon_wf,
abmonoid_wf,
equal_wf,
grp_car_wf,
posint_munit_elim,
decidable__int_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
intEquality,
because_Cache,
natural_numberEquality,
independent_functionElimination,
productElimination
Latex:
\mforall{}a:|<\mBbbZ{}\msupplus{},*>|. Dec(<\mBbbZ{}\msupplus{},*>-unit(a))
Date html generated:
2016_05_16-AM-07_45_47
Last ObjectModification:
2015_12_28-PM-05_53_29
Theory : factor_1
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