Nuprl Lemma : mset_mem_sum
∀s:DSet. ∀a,b:MSet{s}. ∀u:|s|. u ∈b a + b = (u ∈b a) ∨b(u ∈b b)
Proof
Definitions occuring in Statement :
mset_mem: mset_mem,
mset_sum: a + b,
mset: MSet{s},
bor: p ∨bq,
bool: 𝔹,
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
mk_mset: mk_mset(as),
mset_sum: a + b,
mset_mem: mset_mem,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
mem_append,
set_car_wf,
list_wf,
dset_wf,
all_mset_elim,
all_wf,
equal_wf,
bool_wf,
mset_mem_wf,
mset_sum_wf,
mk_mset_wf,
bor_wf,
mset_wf,
sq_stable__all,
sq_stable__equal,
mem_wf,
append_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename,
addLevel,
sqequalRule,
allFunctionality,
lambdaEquality,
independent_functionElimination,
because_Cache,
productElimination,
levelHypothesis,
allLevelFunctionality,
cumulativity,
instantiate,
applyEquality,
universeEquality
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. \mforall{}u:|s|. u \mmember{}\msubb{} a + b = (u \mmember{}\msubb{} a) \mvee{}\msubb{}(u \mmember{}\msubb{} b)
Date html generated:
2016_05_16-AM-07_49_46
Last ObjectModification:
2015_12_28-PM-06_01_39
Theory : mset
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