Nuprl Lemma : list-valueall-type

`∀[T:Type]. valueall-type(T List) supposing valueall-type(T)`

Proof

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

Latex:
\mforall{}[T:Type].  valueall-type(T  List)  supposing  valueall-type(T)

Date html generated: 2017_04_14-AM-08_34_12
Last ObjectModification: 2017_02_27-PM-03_21_55

Theory : list_0

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