Nuprl Lemma : array-model_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. (array-model(AType) ∈ array-model-type{i:l}(AType;Val;n))
Proof
Definitions occuring in Statement :
array-model: array-model(AType),
array-model-type: array-model-type{i:l}(AType;Val;n),
array: array{i:l}(Val;n),
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-model: array-model(AType),
array-model-type: array-model-type{i:l}(AType;Val;n),
let: let,
subtype_rel: A ⊆r B,
M-map: M-map(mnd),
pi1: fst(t),
array-monad: array-monad(AType),
mk_monad: mk_monad(M;return;bind),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
nat: ℕ,
array-monad': array-monad'(AType)
Lemmas referenced :
M-return_wf,
array-monad_wf,
M-bind_wf,
subtype_rel_self,
Arr_wf,
newarray_wf,
pi1_wf,
equal_wf,
M-map_wf,
it_wf,
upd_wf,
unit_wf2,
int_seg_wf,
array-monad'_wf,
idx_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
independent_pairEquality,
isect_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
universeEquality,
lambdaEquality,
functionEquality,
productEquality,
lambdaFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality,
setElimination,
rename,
isectEquality,
instantiate,
functionExtensionality,
axiomEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)].
(array-model(AType) \mmember{} array-model-type\{i:l\}(AType;Val;n))
Date html generated:
2017_10_01-AM-08_43_58
Last ObjectModification:
2017_07_26-PM-04_30_02
Theory : monads
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