Nuprl Lemma : mon_itop_shift
∀[g:IMonoid]. ∀[a,b:ℤ].
∀[E:{a..b-} ⟶ |g|]. ∀[k:ℤ]. ((Π a ≤ j < b. E[j]) = (Π a + k ≤ j < b + k. E[j - k]) ∈ |g|) supposing a ≤ b
Proof
Definitions occuring in Statement :
mon_itop: Π lb ≤ i < ub. E[i],
imon: IMonoid,
grp_car: |g|,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
function: x:A ⟶ B[x],
subtract: n - m,
add: n + m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
mon_itop: Π lb ≤ i < ub. E[i]
Lemmas referenced :
itop_shift
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[g:IMonoid]. \mforall{}[a,b:\mBbbZ{}].
\mforall{}[E:\{a..b\msupminus{}\} {}\mrightarrow{} |g|]. \mforall{}[k:\mBbbZ{}]. ((\mPi{} a \mleq{} j < b. E[j]) = (\mPi{} a + k \mleq{} j < b + k. E[j - k]))
supposing a \mleq{} b
Date html generated:
2016_05_15-PM-00_16_06
Last ObjectModification:
2015_12_26-PM-11_39_46
Theory : groups_1
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