Nuprl Lemma : imax-list-cons
∀[as:ℤ List]. ∀[a:ℤ]. imax-list([a / as]) = imax(a;imax-list(as)) ∈ ℤ supposing 0 < ||as||
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
length: ||as||,
cons: [a / b],
list: T List,
imax: imax(a;b),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
or: P ∨ Q,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
l_exists: (∃x∈L. P[x]),
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
le: A ≤ B
Lemmas referenced :
imax-list-unique,
cons_wf,
imax_wf,
imax-list_wf,
less_than_wf,
length_wf,
list_wf,
l_member_wf,
squash_wf,
true_wf,
imax_unfold,
iff_weakening_equal,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
imax-list-member,
cons_member,
equal-wf-base,
list_subtype_base,
int_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
imax-list-ub,
select_wf,
int_seg_properties,
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,
int_seg_wf,
l_all_cons,
imax_ub
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
productElimination,
natural_numberEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
lambdaFormation,
unionElimination,
equalityElimination,
dependent_functionElimination,
inrFormation,
baseApply,
closedConclusion,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
voidElimination,
inlFormation,
setElimination,
rename,
int_eqEquality,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[as:\mBbbZ{} List]. \mforall{}[a:\mBbbZ{}]. imax-list([a / as]) = imax(a;imax-list(as)) supposing 0 < ||as||
Date html generated:
2017_04_14-AM-09_24_03
Last ObjectModification:
2017_02_27-PM-03_59_12
Theory : list_1
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