Nuprl Lemma : l_contains_append2
∀[T:Type]. ∀A,B:T List. A ⊆ B @ A
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_contains: A ⊆ B,
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
guard: {T},
or: P ∨ Q
Lemmas referenced :
l_all_iff,
l_member_wf,
append_wf,
member_append,
all_wf,
or_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
hypothesis,
setEquality,
productElimination,
independent_functionElimination,
inrFormation,
because_Cache,
addLevel,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}A,B:T List. A \msubseteq{} B @ A
Date html generated:
2019_06_20-PM-01_26_48
Last ObjectModification:
2018_08_24-PM-11_16_44
Theory : list_1
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