Nuprl Lemma : compat-iseg-cases
∀[T:Type]. ∀L1,L2:T List. (L1 || L2 ⇐⇒ L1 < L2 ∨ L2 < L1 ∨ (L1 = L2 ∈ (T List)))
Proof
Definitions occuring in Statement :
proper-iseg: L1 < L2,
compat: l1 || l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
compat: l1 || l2,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
guard: {T},
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
decidable: Dec(P),
cand: A c∧ B,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
intformle_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
iseg_length,
iseg_same_length,
decidable__equal_int,
compat_wf,
iff_wf,
proper-iseg_wf,
proper-iseg-length,
list_wf,
equal_wf,
length_wf,
less_than_wf,
and_wf,
iseg_weakening,
iff_weakening_equal,
true_wf,
squash_wf,
iseg_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
sqequalHypSubstitution,
unionElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
productElimination,
inlFormation,
sqequalRule,
inrFormation,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
addLevel,
impliesFunctionality,
orFunctionality,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. (L1 || L2 \mLeftarrow{}{}\mRightarrow{} L1 < L2 \mvee{} L2 < L1 \mvee{} (L1 = L2))
Date html generated:
2016_05_14-PM-03_05_06
Last ObjectModification:
2016_01_15-AM-07_21_51
Theory : list_1
Home
Index