Nuprl Lemma : intlex_wf
∀[l1,l2:ℤ List]. (l1 ≤_lex l2 ∈ 𝔹)
Proof
Definitions occuring in Statement :
intlex: l1 ≤_lex l2,
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
intlex: l1 ≤_lex l2,
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
bfalse: ff
Lemmas referenced :
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
length_wf_nat,
bor_wf,
lt_int_wf,
length_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
intlex-aux_wf,
equal-wf-base,
list_subtype_base,
int_subtype_base,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
dependent_set_memberEquality,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
equalityTransitivity,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[l1,l2:\mBbbZ{} List]. (l1 \mleq{}\_lex l2 \mmember{} \mBbbB{})
Date html generated:
2017_09_29-PM-05_49_00
Last ObjectModification:
2017_07_26-PM-01_37_22
Theory : list_0
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