### Nuprl Lemma : reduce_wf

`∀[A,B:Type]. ∀[f:A ⟶ B ⟶ B]. ∀[k:B]. ∀[as:A List].  (reduce(f;k;as) ∈ B)`

Proof

Definitions occuring in Statement :  reduce: `reduce(f;k;as)` list: `T List` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  member: `t ∈ T` uall: `∀[x:A]. B[x]` less_than: `a < b` sq_type: `SQType(T)` so_apply: `x[s]` so_lambda: `λ2x.t[x]` it: `⋅` nil: `[]` subtract: `n - m` rev_implies: `P `` Q` iff: `P `⇐⇒` Q` decidable: `Dec(P)` true: `True` less_than': `less_than'(a;b)` not: `¬A` le: `A ≤ B` and: `P ∧ Q` uiff: `uiff(P;Q)` sq_stable: `SqStable(P)` squash: `↓T` so_apply: `x[s1;s2]` so_lambda: `λ2x y.t[x; y]` colength: `colength(L)` cons: `[a / b]` top: `Top` or: `P ∨ Q` subtype_rel: `A ⊆r B` prop: `ℙ` uimplies: `b supposing a` guard: `{T}` ge: `i ≥ j ` false: `False` implies: `P `` Q` nat: `ℕ` all: `∀x:A. B[x]`
Rules used in proof :  Error :universeIsType,  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis because_Cache Error :functionIsType,  Error :inhabitedIsType,  functionEquality universeEquality Error :isect_memberFormation_alt,  sqequalRule axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality functionExtensionality instantiate intEquality minusEquality independent_pairFormation dependent_set_memberEquality addEquality imageElimination baseClosed imageMemberEquality applyLambdaEquality productElimination hypothesis_subsumption promote_hyp voidEquality unionElimination applyEquality cumulativity dependent_functionElimination lambdaEquality voidElimination independent_functionElimination independent_isectElimination natural_numberEquality intWeakElimination rename setElimination lambdaFormation

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[k:B].  \mforall{}[as:A  List].    (reduce(f;k;as)  \mmember{}  B)

Date html generated: 2019_06_20-PM-00_38_51
Last ObjectModification: 2018_09_26-PM-02_05_41

Theory : list_0

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