Nuprl Lemma : mset_mem_inj_sum_lemma
∀a,y,x,s:Top. (x ∈b mset_inj{s}(y) + a ~ (y (=b) x) ∨b(x ∈b a))
Proof
Definitions occuring in Statement :
mset_mem: mset_mem,
mset_sum: a + b,
mset_inj: mset_inj{s}(x),
bor: p ∨bq,
top: Top,
infix_ap: x f y,
all: ∀x:A. B[x],
sqequal: s ~ t,
set_eq: =b
Definitions unfolded in proof :
all: ∀x:A. B[x],
mset_mem: mset_mem,
mset_inj: mset_inj{s}(x),
mset_sum: a + b,
mk_mset: mk_mset(as),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_cons_lemma,
istype-void,
list_ind_nil_lemma,
mem_cons_lemma,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
inhabitedIsType,
hypothesisEquality
Latex:
\mforall{}a,y,x,s:Top. (x \mmember{}\msubb{} mset\_inj\{s\}(y) + a \msim{} (y (=\msubb{}) x) \mvee{}\msubb{}(x \mmember{}\msubb{} a))
Date html generated:
2019_10_16-PM-01_06_28
Last ObjectModification:
2018_10_08-PM-00_20_21
Theory : mset
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