Nuprl Lemma : intlex-reflexive
∀[l1,l2:ℤ List]. l1 ≤_lex l2 = tt supposing l1 = l2 ∈ (ℤ List)
Proof
Definitions occuring in Statement :
intlex: l1 ≤_lex l2,
list: T List,
btrue: tt,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
intlex: l1 ≤_lex l2,
has-value: (a)↓,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
subtype_base_sq,
list_wf,
list_subtype_base,
int_subtype_base,
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
length_wf_nat,
bool_wf,
bool_subtype_base,
equal_wf,
squash_wf,
true_wf,
eq_int_eq_true,
length_wf,
subtype_rel_self,
iff_weakening_equal,
equal-wf-base,
lt_int_wf,
btrue_wf,
bor_tt_simp,
bor_wf,
intlex-aux-reflexive
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
sqequalRule,
callbyvalueReduce,
lambdaEquality,
natural_numberEquality,
because_Cache,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[l1,l2:\mBbbZ{} List]. l1 \mleq{}\_lex l2 = tt supposing l1 = l2
Date html generated:
2019_06_20-PM-00_43_33
Last ObjectModification:
2018_08_31-PM-01_25_22
Theory : list_0
Home
Index