Nuprl Lemma : let_wf
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[x:A]. (let v = x in f[v] ∈ B)
Proof
Definitions occuring in Statement :
let: let,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
let: let,
so_apply: x[s]
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[x:A]. (let v = x in f[v] \mmember{} B)
Date html generated:
2016_05_13-PM-03_14_48
Last ObjectModification:
2016_01_06-PM-05_22_05
Theory : core_2
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