Nuprl Lemma : dlattice-order_weakening
∀[X:Type]. ∀as,bs:X List List. ((as = bs ∈ (X List List)) ⇒ as ⇒ bs)
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,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
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-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
less_than: a < b
Lemmas referenced :
dlattice-order_wf,
squash_wf,
true_wf,
iff_weakening_equal,
l_contains_weakening,
select_wf,
list_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,
l_contains_wf,
int_seg_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_pairFormation,
dependent_functionElimination,
cumulativity,
setElimination,
rename,
unionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[X:Type]. \mforall{}as,bs:X List List. ((as = bs) {}\mRightarrow{} as {}\mRightarrow{} bs)
Date html generated:
2020_05_20-AM-08_26_35
Last ObjectModification:
2017_01_21-PM-04_00_13
Theory : lattices
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