Nuprl Lemma : f-subset_transitivity
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[xs,ys,zs:fset(T)]. (xs ⊆ zs) supposing (ys ⊆ zs and xs ⊆ ys)
Proof
Definitions occuring in Statement :
f-subset: xs ⊆ ys,
fset: fset(T),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
f-subset: xs ⊆ ys,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
fset-member_witness,
fset-member_wf,
all_wf,
isect_wf,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[xs,ys,zs:fset(T)]. (xs \msubseteq{} zs) supposing (ys \msubseteq{} zs and xs \msubseteq{} ys)
Date html generated:
2016_05_14-PM-03_38_28
Last ObjectModification:
2015_12_26-PM-06_42_10
Theory : finite!sets
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