Nuprl Lemma : bsubmset_weakening
∀s:DSet. ∀a,b:MSet{s}. ((a = b ∈ MSet{s}) ⇒ (↑(a ⊆b b)))
Proof
Definitions occuring in Statement :
bsubmset: a ⊆b b,
mset: MSet{s},
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
dset: DSet,
uimplies: b supposing a,
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
equal_mset_elim,
equal_wf,
mset_wf,
mk_mset_wf,
all_mset_elim,
assert_wf,
bsubmset_wf,
sq_stable__all,
sq_stable_from_decidable,
decidable__assert,
all_wf,
dset_wf,
list_wf,
set_car_wf,
permr_wf,
assert_functionality_wrt_uiff,
bsublist_wf,
bsubmset_elim,
bsublist_weakening
Rules used in proof :
cut,
addLevel,
allFunctionality,
impliesFunctionality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
cumulativity,
isectElimination,
sqequalRule,
lambdaEquality,
functionEquality,
lambdaFormation,
because_Cache,
levelHypothesis,
allLevelFunctionality,
impliesLevelFunctionality,
instantiate,
setElimination,
rename,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. ((a = b) {}\mRightarrow{} (\muparrow{}(a \msubseteq{}\msubb{} b)))
Date html generated:
2017_10_01-AM-10_00_22
Last ObjectModification:
2017_03_03-PM-01_01_34
Theory : mset
Home
Index