Nuprl Lemma : all_wf
∀[A:Type]. ∀[B:A ⟶ ℙ]. (∀a:A. B[a] ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
function-wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} \mBbbP{}]. (\mforall{}a:A. B[a] \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_06_58
Last ObjectModification:
2016_01_06-PM-05_28_53
Theory : core_2
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