Nuprl Lemma : A-leftunit
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[T,S:Type]. ∀[x:T]. ∀[f:T ⟶ (A-map S)].
((A-bind(array-model(AType)) (A-return(array-model(AType)) x) f) = (f x) ∈ (A-map S))
Proof
Definitions occuring in Statement :
A-bind: A-bind(AModel),
A-map: A-map,
array-model: array-model(AType),
array: array{i:l}(Val;n),
A-return: A-return(AModel),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
array-model: array-model(AType),
A-return: A-return(AModel),
A-bind: A-bind(AModel),
A-map: A-map,
pi2: snd(t),
pi1: fst(t),
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
M-map_wf,
array-monad_wf,
M-leftunit,
iff_weakening_equal,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
cumulativity,
functionExtensionality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache,
functionEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. \mforall{}[T,S:Type]. \mforall{}[x:T]. \mforall{}[f:T {}\mrightarrow{} (A-map S)].
((A-bind(array-model(AType)) (A-return(array-model(AType)) x) f) = (f x))
Date html generated:
2017_10_01-AM-08_44_05
Last ObjectModification:
2017_07_26-PM-04_30_06
Theory : monads
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