Nuprl Lemma : dlattice-order-append
∀X:Type. ∀a1,b1,a2,b2:X List List. (a1 ⇒ b1 ⇒ a2 ⇒ b2 ⇒ a1 @ a2 ⇒ b1 @ b2)
Proof
Definitions occuring in Statement :
dlattice-order: as ⇒ bs,
append: as @ bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
dlattice-order: as ⇒ bs,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
guard: {T},
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T
Lemmas referenced :
dlattice-order_wf,
list_wf,
l_all_append,
l_exists_wf,
append_wf,
l_contains_wf,
l_member_wf,
or_wf,
l_all_wf2,
l_all_functionality,
l_exists_append,
select_wf,
int_seg_properties,
length_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
because_Cache,
productEquality,
addLevel,
inlFormation,
independent_isectElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageElimination,
inrFormation
Latex:
\mforall{}X:Type. \mforall{}a1,b1,a2,b2:X List List. (a1 {}\mRightarrow{} b1 {}\mRightarrow{} a2 {}\mRightarrow{} b2 {}\mRightarrow{} a1 @ a2 {}\mRightarrow{} b1 @ b2)
Date html generated:
2020_05_20-AM-08_26_38
Last ObjectModification:
2017_01_21-PM-04_23_46
Theory : lattices
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