Nuprl Lemma : compose_wf-injection
∀[A,B,C:Type]. ∀[f:A →⟶ B]. ∀[g:B →⟶ C]. (g o f ∈ A →⟶ C)
Proof
Definitions occuring in Statement :
injection: A →⟶ B,
compose: f o g,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
injection: A →⟶ B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
compose_wf,
inject_wf,
injection_wf,
injection-composition
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[f:A \mrightarrow{}{}\mrightarrow{} B]. \mforall{}[g:B \mrightarrow{}{}\mrightarrow{} C]. (g o f \mmember{} A \mrightarrow{}{}\mrightarrow{} C)
Date html generated:
2016_05_15-PM-06_12_02
Last ObjectModification:
2015_12_27-PM-00_13_04
Theory : general
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