Nuprl Lemma : compose_wf
∀[A,B,C:Type]. ∀[f:B ⟶ C]. ∀[g:A ⟶ B]. (f o g ∈ A ⟶ C)
Proof
Definitions occuring in Statement :
compose: f o g,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
compose: f o g
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
isect_memberEquality,
isectElimination,
thin,
functionEquality,
because_Cache,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[f:B {}\mrightarrow{} C]. \mforall{}[g:A {}\mrightarrow{} B]. (f o g \mmember{} A {}\mrightarrow{} C)
Date html generated:
2019_06_20-PM-00_26_15
Last ObjectModification:
2018_09_26-AM-11_49_08
Theory : fun_1
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