Nuprl Lemma : M-bind_wf
∀[Mnd:Monad]. (M-bind(Mnd) ∈ ⋂T,S:Type. ((M-map(Mnd) T) ⟶ (T ⟶ (M-map(Mnd) S)) ⟶ (M-map(Mnd) S)))
Proof
Definitions occuring in Statement :
M-bind: M-bind(Mnd),
M-map: M-map(mnd),
monad: Monad,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
monad: Monad,
M-bind: M-bind(Mnd),
M-map: M-map(mnd),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
monad_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid
Latex:
\mforall{}[Mnd:Monad]
(M-bind(Mnd) \mmember{} \mcap{}T,S:Type. ((M-map(Mnd) T) {}\mrightarrow{} (T {}\mrightarrow{} (M-map(Mnd) S)) {}\mrightarrow{} (M-map(Mnd) S)))
Date html generated:
2016_05_15-PM-02_16_22
Last ObjectModification:
2015_12_27-AM-08_59_21
Theory : monads
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