Nuprl Lemma : common_iseg_compat
∀[T:Type]. ∀l,l1,l2:T List. (l1 ≤ l ⇒ l2 ≤ l ⇒ l1 || l2)
Proof
Definitions occuring in Statement :
compat: l1 || l2,
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
guard: {T},
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
so_apply: x[s],
le: A ≤ B,
squash: ↓T,
less_than: a < b,
and: P ∧ Q,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
nat: ℕ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
member: t ∈ T,
cand: A c∧ B,
implies: P ⇒ Q,
compat: l1 || l2,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
true: True,
subtype_rel: A ⊆r B
Lemmas referenced :
list_wf,
or_wf,
iseg_wf,
iseg_select,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
select_wf,
equal_wf,
less_than_wf,
isect_wf,
nat_wf,
all_wf,
length_wf,
le_wf,
squash_wf,
true_wf,
istype-int,
istype-void,
subtype_rel_self,
iff_weakening_equal,
istype-le,
istype-nat,
istype-less_than
Rules used in proof :
universeEquality,
functionEquality,
inrFormation,
inlFormation,
addLevel,
imageElimination,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
unionElimination,
natural_numberEquality,
dependent_functionElimination,
independent_isectElimination,
rename,
setElimination,
lambdaEquality,
sqequalRule,
because_Cache,
hypothesis,
hypothesisEquality,
cumulativity,
isectElimination,
extract_by_obid,
introduction,
productEquality,
thin,
productElimination,
sqequalHypSubstitution,
cut,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
Error :inlFormation_alt,
Error :lambdaFormation_alt,
Error :isect_memberFormation_alt,
applyEquality,
Error :lambdaEquality_alt,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
Error :inhabitedIsType,
Error :dependent_pairFormation_alt,
Error :isect_memberEquality_alt,
imageMemberEquality,
baseClosed,
instantiate,
hyp_replacement,
applyLambdaEquality,
Error :productIsType,
Error :functionIsType,
Error :isectIsType,
Error :equalityIstype,
Error :inrFormation_alt
Latex:
\mforall{}[T:Type]. \mforall{}l,l1,l2:T List. (l1 \mleq{} l {}\mRightarrow{} l2 \mleq{} l {}\mRightarrow{} l1 || l2)
Date html generated:
2019_06_20-PM-01_30_08
Last ObjectModification:
2019_01_10-PM-10_10_57
Theory : list_1
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