Nuprl Lemma : f-subset_weakening
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[xs,ys:fset(T)]. xs ⊆ ys supposing xs = ys ∈ fset(T)
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,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
f-subset: xs ⊆ ys,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
fset-member_witness,
fset-member_wf,
f-subset_wf,
equal_wf,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
independent_functionElimination,
cumulativity,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
equalityTransitivity,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[xs,ys:fset(T)]. xs \msubseteq{} ys supposing xs = ys
Date html generated:
2016_10_21-AM-10_44_08
Last ObjectModification:
2016_07_12-AM-05_50_59
Theory : finite!sets
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