Nuprl Lemma : ml_apply_wf
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[x:A]. f(x) ∈ B supposing valueall-type(A)
Proof
Definitions occuring in Statement :
ml_apply: f(x),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ml_apply: f(x),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
valueall-type-has-valueall,
evalall-reduce,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
callbyvalueReduce,
because_Cache,
applyEquality,
functionExtensionality,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[x:A]. f(x) \mmember{} B supposing valueall-type(A)
Date html generated:
2017_09_29-PM-05_50_49
Last ObjectModification:
2017_05_08-PM-02_14_45
Theory : ML
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