### Nuprl Lemma : comb_for_mon_itop_wf

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

Proof

Definitions occuring in Statement :  mon_itop: `Π lb ≤ i < ub. E[i]` imon: `IMonoid` grp_car: `|g|` int_seg: `{i..j-}` so_apply: `x[s]` squash: `↓T` true: `True` member: `t ∈ T` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  member: `t ∈ T` squash: `↓T` uall: `∀[x:A]. B[x]` prop: `ℙ` imon: `IMonoid`
Lemmas referenced :  mon_itop_wf squash_wf true_wf int_seg_wf grp_car_wf imon_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaEquality sqequalHypSubstitution imageElimination cut lemma_by_obid isectElimination thin hypothesisEquality equalityTransitivity hypothesis equalitySymmetry functionEquality setElimination rename intEquality

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

Date html generated: 2016_05_15-PM-00_15_51
Last ObjectModification: 2015_12_26-PM-11_39_50

Theory : groups_1

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