Nuprl Lemma : mset_union_wf_f
∀s:DSet. ∀a,b:FiniteSet{s}. (a ⋃ b ∈ FiniteSet{s})
Proof
Definitions occuring in Statement :
mset_union: a ⋃ b,
finite_set: FiniteSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
guard: {T},
finite_set: FiniteSet{s},
dset: DSet,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
prop: ℙ,
squash: ↓T,
true: True,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q)
Lemmas referenced :
imax_lb,
iff_weakening_equal,
mset_count_union,
true_wf,
squash_wf,
nat_wf,
mset_count_wf,
le_wf,
all_wf,
set_car_wf,
mset_union_wf,
fset_properties,
dset_wf,
finite_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
setElimination,
rename,
dependent_set_memberEquality,
sqequalRule,
lambdaEquality,
applyEquality,
natural_numberEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache,
independent_pairFormation
Latex:
\mforall{}s:DSet. \mforall{}a,b:FiniteSet\{s\}. (a \mcup{} b \mmember{} FiniteSet\{s\})
Date html generated:
2016_05_16-AM-07_51_16
Last ObjectModification:
2016_01_16-PM-11_39_17
Theory : mset
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