Nuprl Lemma : upd_wf

[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)].  (upd(AType) ∈ ℕn ⟶ Val ⟶ Arr(AType) ⟶ Arr(AType))


Proof




Definitions occuring in Statement :  upd: upd(AType) Arr: Arr(AType) array: array{i:l}(Val;n) int_seg: {i..j-} nat: uall: [x:A]. B[x] member: t ∈ T function: x:A ⟶ B[x] natural_number: $n universe: Type
Definitions unfolded in proof :  Arr: Arr(AType) array: array{i:l}(Val;n) uall: [x:A]. B[x] member: t ∈ T upd: upd(AType) pi1: fst(t) pi2: snd(t) prop: nat: subtype_rel: A ⊆B so_lambda: λ2x.t[x] so_apply: x[s] int_seg: {i..j-} all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt ifthenelse: if then else fi  bfalse: ff uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a exists: x:A. B[x] or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b false: False
Lemmas referenced :  int_seg_wf uall_wf equal_wf eq_int_wf bool_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int nat_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productElimination thin functionExtensionality applyEquality hypothesisEquality extract_by_obid sqequalHypSubstitution isectElimination because_Cache hypothesis axiomEquality equalityTransitivity equalitySymmetry productEquality universeEquality functionEquality natural_numberEquality setElimination rename lambdaEquality cumulativity lambdaFormation unionElimination equalityElimination independent_isectElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate independent_functionElimination voidElimination isect_memberEquality

Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[AType:array\{i:l\}(Val;n)].
    (upd(AType)  \mmember{}  \mBbbN{}n  {}\mrightarrow{}  Val  {}\mrightarrow{}  Arr(AType)  {}\mrightarrow{}  Arr(AType))



Date html generated: 2017_10_01-AM-08_43_50
Last ObjectModification: 2017_07_26-PM-04_29_58

Theory : monads


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