Nuprl Lemma : mon_itop_split
∀[g:IMonoid]. ∀[a,b,c:ℤ].
(∀[E:{a..c-} ⟶ |g|]. ((Π a ≤ j < c. E[j]) = ((Π a ≤ j < b. E[j]) * (Π b ≤ j < c. E[j])) ∈ |g|)) supposing
((b ≤ c) and
(a ≤ b))
Proof
Definitions occuring in Statement :
mon_itop: Π lb ≤ i < ub. E[i],
imon: IMonoid,
grp_op: *,
grp_car: |g|,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
le: A ≤ B,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
mon_itop: Π lb ≤ i < ub. E[i]
Lemmas referenced :
itop_split
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[g:IMonoid]. \mforall{}[a,b,c:\mBbbZ{}].
(\mforall{}[E:\{a..c\msupminus{}\} {}\mrightarrow{} |g|]
((\mPi{} a \mleq{} j < c. E[j]) = ((\mPi{} a \mleq{} j < b. E[j]) * (\mPi{} b \mleq{} j < c. E[j])))) supposing
((b \mleq{} c) and
(a \mleq{} b))
Date html generated:
2016_05_15-PM-00_16_11
Last ObjectModification:
2015_12_26-PM-11_39_40
Theory : groups_1
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