Nuprl Lemma : comb_for_compose_wf_for_mon_hom
λA,B,C,f,g,z. (g o f) ∈ A:IMonoid ⟶ B:IMonoid ⟶ C:IMonoid ⟶ f:MonHom(A,B) ⟶ g:MonHom(B,C) ⟶ (↓True) ⟶ MonHom(A,C)
Proof
Definitions occuring in Statement :
monoid_hom: MonHom(M1,M2),
imon: IMonoid,
compose: f o 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 :
compose_wf_for_mon_hom,
squash_wf,
true_wf,
monoid_hom_wf,
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{}A,B,C,f,g,z. (g o f) \mmember{} A:IMonoid
{}\mrightarrow{} B:IMonoid
{}\mrightarrow{} C:IMonoid
{}\mrightarrow{} f:MonHom(A,B)
{}\mrightarrow{} g:MonHom(B,C)
{}\mrightarrow{} (\mdownarrow{}True)
{}\mrightarrow{} MonHom(A,C)
Date html generated:
2016_05_15-PM-00_10_36
Last ObjectModification:
2015_12_26-PM-11_44_33
Theory : groups_1
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