Nuprl Lemma : bag-inject_wf
∀[A,B:Type]. ∀[b:bag(A)]. ∀[f:A ⟶ B]. (bag-inject(A;b;B;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
bag-inject: bag-inject(A;b;B;f),
bag: bag(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-inject: bag-inject(A;b;B;f),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
inject_wf,
bag-member_wf,
subtype_rel_dep_function,
set_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[b:bag(A)]. \mforall{}[f:A {}\mrightarrow{} B]. (bag-inject(A;b;B;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-02_42_03
Last ObjectModification:
2015_12_27-AM-09_39_57
Theory : bags
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