Nuprl Lemma : mset_inter_comm
∀s:DSet. ∀a,b:MSet{s}. ((a ⋂s b) = (b ⋂s a) ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_inter: a ⋂s b,
mset: MSet{s},
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
dset: DSet,
so_lambda: λ2x.t[x],
true: True,
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
nat: ℕ
Lemmas referenced :
nat_wf,
mset_count_wf,
imin_com,
dset_wf,
mset_wf,
iff_weakening_equal,
mset_count_inter,
equal_wf,
set_car_wf,
true_wf,
squash_wf,
all_wf,
mset_inter_wf,
eq_mset_iff_eq_counts
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
intEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. ((a \mcap{}s b) = (b \mcap{}s a))
Date html generated:
2016_05_16-AM-07_49_36
Last ObjectModification:
2016_01_16-PM-11_39_40
Theory : mset
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