Nuprl Lemma : uall_wf
∀[A:Type]. ∀[B:A ⟶ ℙ]. (∀[x:A]. B[x] ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
prop: ℙ,
so_apply: x[s]
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
isectEquality,
cumulativity,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
universeEquality,
isect_memberEquality,
isectElimination,
thin
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} \mBbbP{}]. (\mforall{}[x:A]. B[x] \mmember{} \mBbbP{})
Date html generated:
2018_05_21-AM-11_59_56
Last ObjectModification:
2018_02_02-AM-09_38_28
Theory : core_2
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