Nuprl Lemma : M-leftunit
∀[Mnd:Monad]. ∀[T,S:Type]. ∀[x:T]. ∀[f:T ⟶ (M-map(Mnd) S)].
((M-bind(Mnd) (M-return(Mnd) x) f) = (f x) ∈ (M-map(Mnd) S))
Proof
Definitions occuring in Statement :
M-bind: M-bind(Mnd),
M-return: M-return(Mnd),
M-map: M-map(mnd),
monad: Monad,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
monad: Monad,
M-return: M-return(Mnd),
M-bind: M-bind(Mnd),
M-map: M-map(mnd),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
M-map_wf,
monad_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
functionEquality,
hypothesisEquality,
applyEquality,
lemma_by_obid,
isectElimination,
isect_memberEquality,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[Mnd:Monad]. \mforall{}[T,S:Type]. \mforall{}[x:T]. \mforall{}[f:T {}\mrightarrow{} (M-map(Mnd) S)].
((M-bind(Mnd) (M-return(Mnd) x) f) = (f x))
Date html generated:
2016_05_15-PM-02_16_23
Last ObjectModification:
2015_12_27-AM-08_59_27
Theory : monads
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