Nuprl Lemma : l_member_subtype2
∀[A,B:Type]. ∀L:A List. ∀x:A. {(x ∈ L) ⇒ (x ∈ L)} supposing A ⊆r B
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
guard: {T}
Lemmas referenced :
l_member_subtype
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[A,B:Type]. \mforall{}L:A List. \mforall{}x:A. \{(x \mmember{} L) {}\mRightarrow{} (x \mmember{} L)\} supposing A \msubseteq{}r B
Date html generated:
2016_05_14-AM-07_49_36
Last ObjectModification:
2015_12_26-PM-04_45_31
Theory : list_1
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