Nuprl Lemma : gcd-reduce-eq-constraints_wf
∀[LL,sat:ℤ List+ List]. (gcd-reduce-eq-constraints(sat;LL) ∈ ℤ List+ List?)
Proof
Definitions occuring in Statement :
gcd-reduce-eq-constraints: gcd-reduce-eq-constraints(sat;LL),
listp: A List+,
list: T List,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
union: left + right,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
gcd-reduce-eq-constraints: gcd-reduce-eq-constraints(sat;LL),
so_lambda: λ2x y.t[x; y],
listp: A List+,
all: ∀x:A. B[x],
or: P ∨ Q,
nil: [],
it: ⋅,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
and: P ∧ Q,
cons: [a / b],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
not: ¬A,
nequal: a ≠ b ∈ T ,
has-value: (a)↓,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
top: Top,
true: True,
int_nzero: ℤ-o,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
le: A ≤ B,
prop: ℙ,
so_apply: x[s1;s2]
Lemmas referenced :
accumulate_abort_wf,
listp_wf,
list_wf,
unit_wf2,
list-cases,
length_of_nil_lemma,
product_subtype_list,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
cons_wf,
cons-listp,
nil_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
it_wf,
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
absval_wf,
gcd-list_wf,
lt_int_wf,
assert_of_lt_int,
istype-top,
istype-void,
eager_map_cons_lemma,
remainder_wfa,
not-equal-2,
decidable__le,
istype-le,
istype-false,
not-le-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
zero-add,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
nequal_wf,
divide_wfa,
eager-map_wf,
list-value-type,
iff_weakening_uiff,
assert_wf,
less_than_wf,
istype-less_than,
list-valueall-type,
set-valueall-type,
length_wf,
int-valueall-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
intEquality,
hypothesis,
because_Cache,
Error :inlEquality_alt,
hypothesisEquality,
Error :universeIsType,
Error :lambdaEquality_alt,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
natural_numberEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
equalityElimination,
independent_isectElimination,
int_eqReduceTrueSq,
equalityTransitivity,
equalitySymmetry,
Error :dependent_pairFormation_alt,
Error :equalityIstype,
instantiate,
cumulativity,
independent_functionElimination,
int_eqReduceFalseSq,
Error :inrEquality_alt,
callbyvalueReduce,
applyEquality,
lessCases,
axiomSqEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
independent_pairFormation,
imageMemberEquality,
baseClosed,
Error :dependent_set_memberEquality_alt,
addEquality,
Error :inlFormation_alt,
Error :inrFormation_alt,
minusEquality,
axiomEquality
Latex:
\mforall{}[LL,sat:\mBbbZ{} List\msupplus{} List]. (gcd-reduce-eq-constraints(sat;LL) \mmember{} \mBbbZ{} List\msupplus{} List?)
Date html generated:
2019_06_20-PM-00_48_06
Last ObjectModification:
2019_03_06-PM-09_58_32
Theory : omega
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