### Nuprl Lemma : comb_for_mon_nat_op_wf2

`λg,n,e,z. (n ⋅ e) ∈ g:IMonoid ⟶ n:|(<ℤ+>↓hgrp)| ⟶ e:|g| ⟶ (↓True) ⟶ |g|`

Proof

Definitions occuring in Statement :  int_add_grp: `<ℤ+>` mon_nat_op: `n ⋅ e` hgrp_of_ocgrp: `g↓hgrp` imon: `IMonoid` grp_car: `|g|` squash: `↓T` true: `True` member: `t ∈ T` lambda: `λx.A[x]` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  member: `t ∈ T` squash: `↓T` uall: `∀[x:A]. B[x]` prop: `ℙ` imon: `IMonoid`
Lemmas referenced :  mon_nat_op_wf2 squash_wf true_wf grp_car_wf hgrp_of_ocgrp_wf int_add_grp_wf2 imon_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaEquality sqequalHypSubstitution imageElimination cut lemma_by_obid isectElimination thin hypothesisEquality equalityTransitivity hypothesis equalitySymmetry setElimination rename

Latex:
\mlambda{}g,n,e,z.  (n  \mcdot{}  e)  \mmember{}  g:IMonoid  {}\mrightarrow{}  n:|(<\mBbbZ{}+>\mdownarrow{}hgrp)|  {}\mrightarrow{}  e:|g|  {}\mrightarrow{}  (\mdownarrow{}True)  {}\mrightarrow{}  |g|

Date html generated: 2016_05_15-PM-00_19_54
Last ObjectModification: 2015_12_26-PM-11_37_46

Theory : groups_1

Home Index