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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