Nuprl Lemma : A-null-property
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)].
∀A:Arr(AType). ∀k:ℕn. (A-post-val(AType;A-null(AType);A;k) = A-pre-val(AType;A;k) ∈ Val)
Proof
Definitions occuring in Statement :
A-null: A-null(AType),
A-post-val: A-post-val(AType;prog;A;i),
Arr: Arr(AType),
array: array{i:l}(Val;n),
A-pre-val: A-pre-val(AType;A;i),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
A-pre-val: A-pre-val(AType;A;i),
A-null: A-null(AType),
A-post-val: A-post-val(AType;prog;A;i),
nat: ℕ,
array: array{i:l}(Val;n),
Arr: Arr(AType),
pi1: fst(t),
idx: idx(AType),
array-model: array-model(AType),
A-fetch': A-fetch'(AModel),
A-coerce: A-coerce(AModel),
A-return: A-return(AModel),
A-bind: A-bind(AModel),
A-eval: A-eval(AModel),
pi2: snd(t),
array-monad: array-monad(AType),
M-return: M-return(Mnd),
M-bind: M-bind(Mnd),
let: let,
mk_monad: mk_monad(M;return;bind)
Lemmas referenced :
int_seg_wf,
Arr_wf,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
because_Cache,
isect_memberEquality,
universeEquality,
productElimination,
applyEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)].
\mforall{}A:Arr(AType). \mforall{}k:\mBbbN{}n. (A-post-val(AType;A-null(AType);A;k) = A-pre-val(AType;A;k))
Date html generated:
2016_05_15-PM-02_19_19
Last ObjectModification:
2015_12_27-AM-08_58_19
Theory : monads
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