Nuprl Lemma : omega_step_wf
∀[p:IntConstraints]. (omega_step(p) ∈ IntConstraints)
Proof
Definitions occuring in Statement :
omega_step: omega_step(p),
int-constraint-problem: IntConstraints,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
omega_step: omega_step(p),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
less_than: a < b,
less_than': less_than'(a;b),
top: Top,
true: True,
squash: ↓T,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
prop: ℙ,
int-constraint-problem: IntConstraints,
tunion: ⋃x:A.B[x],
pi2: snd(t),
int-problem-dimension: dim(p),
decidable: Dec(P),
so_lambda: λ2x.t[x],
so_apply: x[s],
nil: [],
cons: [a / b],
subtract: n - m,
int_seg: {i..j-},
sq_stable: SqStable(P),
lelt: i ≤ j < k,
le: A ≤ B,
int_upper: {i...}
Lemmas referenced :
lt_int_wf,
int-problem-dimension_wf,
eqtt_to_assert,
assert_of_lt_int,
istype-top,
istype-void,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
int-constraint-problem_wf,
decidable__equal_int,
int_subtype_base,
set_wf,
list_wf,
equal_wf,
length_wf,
list-cases,
product_subtype_list,
reduce_hd_cons_lemma,
subtract_wf,
first-success_wf,
equal-wf-base-T,
list_subtype_base,
equal-wf-base,
int_seg_wf,
equal-wf-T-base,
absval_wf,
select_wf,
decidable__le,
istype-false,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
istype-int,
find-exact-eq-constraint_wf,
decidable__lt,
not-lt-2,
le_antisymmetry_iff,
add-swap,
add-zero,
exact-reduce-constraints_wf2,
set_subtype_base,
lelt_wf,
gcd-reduce-eq-constraints_wf2,
not-equal-2,
minus-zero,
minus-minus,
le_wf,
nil_wf,
gcd-reduce-ineq-constraints_wf2,
unit_wf2,
subtype_rel_union,
tunion_wf,
nat_wf,
null_wf,
assert_of_null,
shadow_inequalities_wf,
le-add-cancel2,
subtype_rel_list_set,
eager-map-is-map,
list-value-type,
eager-map_wf,
int-value-type,
append_wf,
map_wf,
map-length
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
sqequalRule,
natural_numberEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
Error :lambdaEquality_alt,
setElimination,
rename,
lessCases,
axiomSqEquality,
Error :isect_memberEquality_alt,
independent_pairFormation,
voidElimination,
imageMemberEquality,
baseClosed,
imageElimination,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :equalityIsType1,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
Error :universeIsType,
axiomEquality,
intEquality,
addEquality,
hypothesis_subsumption,
setEquality,
baseApply,
closedConclusion,
productEquality,
minusEquality,
Error :setIsType,
Error :equalityIsType4,
Error :dependent_set_memberEquality_alt,
applyLambdaEquality,
Error :inlEquality_alt,
Error :inrEquality_alt,
voidEquality,
Error :dependent_pairEquality_alt,
independent_pairEquality,
Error :productIsType
Latex:
\mforall{}[p:IntConstraints]. (omega\_step(p) \mmember{} IntConstraints)
Date html generated:
2019_06_20-PM-00_51_13
Last ObjectModification:
2018_10_02-PM-05_40_47
Theory : omega
Home
Index