Nuprl Lemma : mon_itop_unroll_unit

[g:IMonoid]. ∀[i,j:ℤ].  ∀[E:{i..j-} ⟶ |g|]. ((Π i ≤ k < j. E[k]) E[i] ∈ |g|) supposing (i 1) j ∈ ℤ


Proof




Definitions occuring in Statement :  mon_itop: Π lb ≤ i < ub. E[i] imon: IMonoid grp_car: |g| int_seg: {i..j-} uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] function: x:A ⟶ B[x] add: m natural_number: $n int: equal: t ∈ T
Definitions unfolded in proof :  mon_itop: Π lb ≤ i < ub. E[i]
Lemmas referenced :  itop_unroll_unit
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])  supposing  (i  +  1)  =  j



Date html generated: 2016_05_15-PM-00_16_01
Last ObjectModification: 2015_12_26-PM-11_40_01

Theory : groups_1


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