Nuprl Lemma : dlattice-order_transitivity
∀[X:Type]. ∀as,bs,cs:X List List. (as ⇒ bs ⇒ bs ⇒ cs ⇒ as ⇒ cs)
Proof
Definitions occuring in Statement :
dlattice-order: as ⇒ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
dlattice-order: as ⇒ bs,
l_all: (∀x∈L.P[x]),
l_exists: (∃x∈L. P[x]),
exists: ∃x:A. B[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T
Lemmas referenced :
dlattice-order_wf,
list_wf,
int_seg_wf,
length_wf,
l_contains_wf,
select_wf,
int_seg_properties,
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,
l_contains_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
dependent_functionElimination,
productElimination,
rename,
natural_numberEquality,
dependent_pairFormation,
because_Cache,
setElimination,
independent_isectElimination,
unionElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
imageElimination,
independent_functionElimination
Latex:
\mforall{}[X:Type]. \mforall{}as,bs,cs:X List List. (as {}\mRightarrow{} bs {}\mRightarrow{} bs {}\mRightarrow{} cs {}\mRightarrow{} as {}\mRightarrow{} cs)
Date html generated:
2020_05_20-AM-08_26_33
Last ObjectModification:
2017_01_21-PM-03_59_35
Theory : lattices
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