Nuprl Lemma : flattice-order-append
∀X:Type. ∀a1,b1,as,bs:(X + X) List List.
(flattice-order(X;a1;b1) ⇒ flattice-order(X;as;bs) ⇒ flattice-order(X;a1 @ as;b1 @ bs))
Proof
Definitions occuring in Statement :
flattice-order: flattice-order(X;as;bs),
append: as @ bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
flattice-order: flattice-order(X;as;bs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
or: P ∨ Q,
guard: {T},
cand: A c∧ B
Lemmas referenced :
l_all_iff,
list_wf,
l_member_wf,
or_wf,
l_exists_wf,
equal_wf,
flip-union_wf,
l_contains_wf,
append_wf,
l_exists_iff,
exists_wf,
member_append,
all_wf,
flattice-order_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
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,
impliesFunctionality,
existsFunctionality,
independent_pairFormation,
andLevelFunctionality,
existsLevelFunctionality,
functionEquality,
universeEquality,
unionElimination,
inlFormation,
inrFormation,
dependent_pairFormation
Latex:
\mforall{}X:Type. \mforall{}a1,b1,as,bs:(X + X) List List.
(flattice-order(X;a1;b1) {}\mRightarrow{} flattice-order(X;as;bs) {}\mRightarrow{} flattice-order(X;a1 @ as;b1 @ bs))
Date html generated:
2020_05_20-AM-08_59_26
Last ObjectModification:
2017_01_24-AM-10_50_52
Theory : lattices
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