Nuprl Lemma : flattice-order_transitivity
∀[X:Type]. ∀as,bs,cs:(X + X) List List. (flattice-order(X;as;bs) ⇒ flattice-order(X;bs;cs) ⇒ flattice-order(X;as;cs))
Proof
Definitions occuring in Statement :
flattice-order: flattice-order(X;as;bs),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
flattice-order: flattice-order(X;as;bs),
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
or: P ∨ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
guard: {T}
Lemmas referenced :
l_all_iff,
list_wf,
l_member_wf,
or_wf,
l_exists_wf,
equal_wf,
flip-union_wf,
l_contains_wf,
l_exists_iff,
exists_wf,
all_wf,
flattice-order_wf,
l_contains-member,
l_contains_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
unionEquality,
cumulativity,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
because_Cache,
setEquality,
productElimination,
independent_functionElimination,
allFunctionality,
addLevel,
orFunctionality,
productEquality,
promote_hyp,
unionElimination,
inlFormation,
dependent_pairFormation,
independent_pairFormation,
inrFormation,
impliesFunctionality,
functionEquality,
universeEquality
Latex:
\mforall{}[X:Type]
\mforall{}as,bs,cs:(X + X) List List.
(flattice-order(X;as;bs) {}\mRightarrow{} flattice-order(X;bs;cs) {}\mRightarrow{} flattice-order(X;as;cs))
Date html generated:
2020_05_20-AM-08_59_22
Last ObjectModification:
2017_07_28-AM-09_18_11
Theory : lattices
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