Nuprl Lemma : p_subset_wf
∀[T:Type]. ∀[A,B:T ⟶ ℙ]. (A ⊆{T} B ∈ ℙ)
Proof
Definitions occuring in Statement :
p_subset: A ⊆{T} B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
p_subset: A ⊆{T} B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[A,B:T {}\mrightarrow{} \mBbbP{}]. (A \msubseteq{}\{T\} B \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_00_16
Last ObjectModification:
2015_12_26-PM-11_26_49
Theory : gen_algebra_1
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