Nuprl Lemma : A-assign_wf

[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)].  (A-assign(array-model(AType)) ∈ ℕn ⟶ Val ⟶ (A-map Unit))


Proof




Definitions occuring in Statement :  A-assign: A-assign(AModel) A-map: A-map array-model: array-model(AType) array: array{i:l}(Val;n) int_seg: {i..j-} nat: uall: [x:A]. B[x] unit: Unit member: t ∈ T apply: a function: x:A ⟶ B[x] natural_number: $n universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T array-model: array-model(AType) A-assign: A-assign(AModel) A-map: A-map pi2: snd(t) pi1: fst(t) array-monad: array-monad(AType) M-map: M-map(mnd) mk_monad: mk_monad(M;return;bind) nat:
Lemmas referenced :  array_wf nat_wf it_wf upd_wf Arr_wf int_seg_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry lemma_by_obid isectElimination thin hypothesisEquality isect_memberEquality because_Cache universeEquality lambdaEquality independent_pairEquality applyEquality natural_numberEquality setElimination rename

Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[AType:array\{i:l\}(Val;n)].
    (A-assign(array-model(AType))  \mmember{}  \mBbbN{}n  {}\mrightarrow{}  Val  {}\mrightarrow{}  (A-map  Unit))



Date html generated: 2016_05_15-PM-02_18_39
Last ObjectModification: 2015_12_27-AM-08_58_43

Theory : monads


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