Nuprl Lemma : spread-wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[C:a:A ⟶ b:B[a] ⟶ Type]. ∀[p:a:A × B[a]]. ∀[F:a:A ⟶ b:B[a] ⟶ C[a;b]].
(let x,y = p
in F[x;y] ∈ C[fst(p);snd(p)])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
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],
subtype_rel: A ⊆r B,
pi1: fst(t),
pi2: snd(t),
so_apply: x[s]
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
spreadEquality,
hypothesisEquality,
applyEquality,
hypothesis,
lambdaEquality,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
productEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[C:a:A {}\mrightarrow{} b:B[a] {}\mrightarrow{} Type]. \mforall{}[p:a:A \mtimes{} B[a]].
\mforall{}[F:a:A {}\mrightarrow{} b:B[a] {}\mrightarrow{} C[a;b]].
(let x,y = p
in F[x;y] \mmember{} C[fst(p);snd(p)])
Date html generated:
2016_05_15-PM-03_21_52
Last ObjectModification:
2015_12_27-PM-01_04_32
Theory : general
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