### Nuprl Lemma : mon_itop_wf

`∀[g:IMonoid]. ∀[p,q:ℤ]. ∀[E:{p..q-} ⟶ |g|].  (Π p ≤ i < q. E[i] ∈ |g|)`

Proof

Definitions occuring in Statement :  mon_itop: `Π lb ≤ i < ub. E[i]` imon: `IMonoid` grp_car: `|g|` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  mon_itop: `Π lb ≤ i < ub. E[i]` uall: `∀[x:A]. B[x]` member: `t ∈ T` imon: `IMonoid` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  itop_wf grp_car_wf grp_op_wf grp_id_wf int_seg_wf imon_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis lambdaEquality applyEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality because_Cache intEquality

Latex:
\mforall{}[g:IMonoid].  \mforall{}[p,q:\mBbbZ{}].  \mforall{}[E:\{p..q\msupminus{}\}  {}\mrightarrow{}  |g|].    (\mPi{}  p  \mleq{}  i  <  q.  E[i]  \mmember{}  |g|)

Date html generated: 2016_05_15-PM-00_15_47
Last ObjectModification: 2015_12_26-PM-11_40_09

Theory : groups_1

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