Nuprl Lemma : array-monad_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. (array-monad(AType) ∈ Monad)
Proof
Definitions occuring in Statement :
array-monad: array-monad(AType),
array: array{i:l}(Val;n),
monad: Monad,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
array-monad: array-monad(AType),
let: let,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
pi1: fst(t),
pi2: snd(t),
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mk_monad_wf,
Arr_wf,
pi1_wf,
equal_wf,
pi2_wf,
squash_wf,
true_wf,
eta_conv,
iff_weakening_equal,
pair_eta_rw,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
functionEquality,
cumulativity,
hypothesisEquality,
hypothesis,
productEquality,
because_Cache,
universeEquality,
isect_memberEquality,
independent_pairEquality,
applyEquality,
functionExtensionality,
lambdaFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
independent_isectElimination,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. (array-monad(AType) \mmember{} Monad)
Date html generated:
2017_10_01-AM-08_43_55
Last ObjectModification:
2017_07_26-PM-04_30_00
Theory : monads
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