Nuprl Lemma : mon_itop_unroll_lo
∀[g:IMonoid]. ∀[i,j:ℤ].
∀[E:{i..j-} ⟶ |g|]. ((Π i ≤ k < j. E[k]) = (E[i] * (Π i + 1 ≤ k < j. E[k])) ∈ |g|) supposing i < j
Proof
Definitions occuring in Statement :
mon_itop: Π lb ≤ i < ub. E[i],
imon: IMonoid,
grp_op: *,
grp_car: |g|,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
mon_itop: Π lb ≤ i < ub. E[i]
Lemmas referenced :
itop_unroll_lo
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[g:IMonoid]. \mforall{}[i,j:\mBbbZ{}].
\mforall{}[E:\{i..j\msupminus{}\} {}\mrightarrow{} |g|]. ((\mPi{} i \mleq{} k < j. E[k]) = (E[i] * (\mPi{} i + 1 \mleq{} k < j. E[k]))) supposing i < j
Date html generated:
2016_05_15-PM-00_16_04
Last ObjectModification:
2015_12_26-PM-11_39_54
Theory : groups_1
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