Nuprl Lemma : mcompose_wf
∀[X,Y,Z:Type].
∀dx:metric(X). ∀dy:metric(Y). ∀dz:metric(Z). ∀[f:FUN(X ⟶ Y)]. ∀[g:FUN(Y ⟶ Z)]. (mcompose(f;g) ∈ FUN(X ⟶ Z))
Proof
Definitions occuring in Statement :
mcompose: mcompose(f;g),
mfun: FUN(X ⟶ Y),
metric: metric(X),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
mcompose: mcompose(f;g),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Latex:
\mforall{}[X,Y,Z:Type].
\mforall{}dx:metric(X). \mforall{}dy:metric(Y). \mforall{}dz:metric(Z).
\mforall{}[f:FUN(X {}\mrightarrow{} Y)]. \mforall{}[g:FUN(Y {}\mrightarrow{} Z)]. (mcompose(f;g) \mmember{} FUN(X {}\mrightarrow{} Z))
Date html generated:
2020_05_20-AM-11_40_33
Last ObjectModification:
2019_11_20-PM-02_13_04
Theory : reals
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