Nuprl Lemma : set-equal_wf
∀[T:Type]. ∀[x,y:T List]. (set-equal(T;x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
set-equal: set-equal(T;x;y),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
set-equal: set-equal(T;x;y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
all_wf,
iff_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:T List]. (set-equal(T;x;y) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-01_37_15
Last ObjectModification:
2015_12_26-PM-05_28_02
Theory : list_1
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