Nuprl Lemma : posint_munit_elim
∀a:|<ℤ+,*>|. (<ℤ+,*>-unit(a) ⇐⇒ a = 1 ∈ ℤ)
Proof
Definitions occuring in Statement :
posint_mul_mon: <ℤ+,*>,
munit: g-unit(u),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T,
grp_car: |g|
Definitions unfolded in proof :
munit: g-unit(u),
mdivides: b | a,
posint_mul_mon: <ℤ+,*>,
grp_car: |g|,
pi1: fst(t),
grp_id: e,
pi2: snd(t),
grp_op: *,
infix_ap: x f y,
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
mul_nat_plus,
equal-wf-base-T,
exists_wf,
less_than_wf,
divides_nchar,
iff_wf,
divides_wf,
le_wf,
false_wf,
nat_plus_subtype_nat,
assoced_nelim,
unit_chars,
equal_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
hypothesis,
independent_pairFormation,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
because_Cache,
addLevel,
productElimination,
independent_functionElimination,
dependent_functionElimination,
applyEquality,
dependent_set_memberEquality,
impliesFunctionality,
equalityTransitivity,
equalitySymmetry,
introduction,
imageMemberEquality,
baseClosed,
lambdaEquality
Latex:
\mforall{}a:|<\mBbbZ{}\msupplus{},*>|. (<\mBbbZ{}\msupplus{},*>-unit(a) \mLeftarrow{}{}\mRightarrow{} a = 1)
Date html generated:
2016_05_16-AM-07_45_36
Last ObjectModification:
2016_01_16-PM-11_37_49
Theory : factor_1
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