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
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