Nuprl Lemma : spread_wf
∀[A,B,C:Type]. ∀[p:A × B]. ∀[F:A ⟶ B ⟶ C]. (let x,y = p in F[x;y] ∈ C)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
spread: spread def,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s1;s2]
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
spreadEquality,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
productEquality,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[p:A \mtimes{} B]. \mforall{}[F:A {}\mrightarrow{} B {}\mrightarrow{} C]. (let x,y = p in F[x;y] \mmember{} C)
Date html generated:
2016_05_15-PM-03_21_47
Last ObjectModification:
2015_12_27-PM-01_04_28
Theory : general
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