Nuprl Lemma : forall_wf
∀[A:Type]. ∀[B:A ⟶ ℙ]. (∀a.B[a] ∈ ℙ)
Proof
Definitions occuring in Statement :
forall: ∀x.P[x],
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,
forall: ∀x.P[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} \mBbbP{}]. (\mforall{}a.B[a] \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-09_07_31
Last ObjectModification:
2015_12_28-PM-07_02_59
Theory : first-order!and!ancestral!logic
Home
Index