Nuprl Lemma : is-mfun-compose
∀[X,Y,Z:Type]. ∀[d:metric(X)]. ∀[d':metric(Y)]. ∀[d'':metric(Z)]. ∀[f:X ⟶ Y]. ∀[g:Y ⟶ Z].
(g o f:FUN(X;Z)) supposing (g:FUN(Y;Z) and f:FUN(X;Y))
Proof
Definitions occuring in Statement :
is-mfun: f:FUN(X;Y),
metric: metric(X),
compose: f o g,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
is-mfun: f:FUN(X;Y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
compose: f o g,
prop: ℙ,
meq: x ≡ y,
metric: metric(X)
Latex:
\mforall{}[X,Y,Z:Type]. \mforall{}[d:metric(X)]. \mforall{}[d':metric(Y)]. \mforall{}[d'':metric(Z)]. \mforall{}[f:X {}\mrightarrow{} Y]. \mforall{}[g:Y {}\mrightarrow{} Z].
(g o f:FUN(X;Z)) supposing (g:FUN(Y;Z) and f:FUN(X;Y))
Date html generated:
2020_05_20-AM-11_39_55
Last ObjectModification:
2019_11_15-PM-03_13_22
Theory : reals
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