Nuprl Lemma : bsubmset_transitivity
∀s:DSet. ∀a,b,c:MSet{s}. ((↑(a ⊆b b)) ⇒ (↑(b ⊆b c)) ⇒ (↑(a ⊆b c)))
Proof
Definitions occuring in Statement :
bsubmset: a ⊆b b,
mset: MSet{s},
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
dset: DSet,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
all_mset_elim,
assert_wf,
bsubmset_wf,
mk_mset_wf,
mset_wf,
sq_stable__all,
sq_stable_from_decidable,
decidable__assert,
all_wf,
dset_wf,
list_wf,
set_car_wf,
assert_functionality_wrt_uiff,
bsublist_wf,
bsubmset_elim,
bsublist_transitivity
Rules used in proof :
cut,
addLevel,
allFunctionality,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
functionEquality,
isectElimination,
hypothesis,
independent_functionElimination,
lambdaFormation,
productElimination,
because_Cache,
levelHypothesis,
allLevelFunctionality,
cumulativity,
instantiate,
setElimination,
rename,
applyEquality,
universeEquality,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}a,b,c:MSet\{s\}. ((\muparrow{}(a \msubseteq{}\msubb{} b)) {}\mRightarrow{} (\muparrow{}(b \msubseteq{}\msubb{} c)) {}\mRightarrow{} (\muparrow{}(a \msubseteq{}\msubb{} c)))
Date html generated:
2016_05_16-AM-07_50_47
Last ObjectModification:
2015_12_28-PM-06_01_19
Theory : mset
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