Nuprl Lemma : bag-eq-subtype
∀[A:Type]. ∀[d1,d2:bag(A)]. d1 = d2 ∈ bag({a:A| a ↓∈ d1} ) supposing d1 = d2 ∈ bag(A)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
uimplies: b supposing a,
true: True,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q
Lemmas referenced :
bag-eq-subtype1,
bag-member_wf,
bag-subtype,
set_wf,
equal_wf,
bag_wf,
member_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
cumulativity,
equalityTransitivity,
hypothesis,
equalitySymmetry,
sqequalRule,
dependent_functionElimination,
because_Cache,
hyp_replacement,
Error :applyLambdaEquality,
instantiate,
universeEquality,
setEquality,
independent_isectElimination,
natural_numberEquality,
isect_memberFormation,
isect_memberEquality,
axiomEquality,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[d1,d2:bag(A)]. d1 = d2 supposing d1 = d2
Date html generated:
2016_10_25-AM-10_31_28
Last ObjectModification:
2016_07_12-AM-06_47_30
Theory : bags
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