Nuprl Lemma : free_abmon_umap_wf
∀S:DSet. ∀f:FAbMon(S).
(f.umap ∈ mon':AbMon ⟶ f':(|S| ⟶ |mon'|) ⟶ {!g:MonHom(f.mon,mon') | (g o f.inj) = f' ∈ (|S| ⟶ |mon'|)})
Proof
Definitions occuring in Statement :
free_abmon_umap: f.umap,
free_abmon_inj: f.inj,
free_abmon_mon: f.mon,
free_abmonoid: FAbMon(S),
compose: f o g,
unique_set: {!x:T | P[x]},
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
equal: s = t ∈ T,
monoid_hom: MonHom(M1,M2),
abmonoid: AbMon,
grp_car: |g|,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
free_abmonoid: FAbMon(S),
free_abmon_umap: f.umap,
free_abmon_inj: f.inj,
free_abmon_mon: f.mon,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
free_abmonoid_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
lemma_by_obid,
dependent_functionElimination
Latex:
\mforall{}S:DSet. \mforall{}f:FAbMon(S).
(f.umap \mmember{} mon':AbMon {}\mrightarrow{} f':(|S| {}\mrightarrow{} |mon'|) {}\mrightarrow{} \{!g:MonHom(f.mon,mon') | (g o f.inj) = f'\})
Date html generated:
2016_05_16-AM-07_48_29
Last ObjectModification:
2015_12_28-PM-06_02_14
Theory : mset
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