Nuprl Lemma : fan-implies-nwkl!-using-PFan
Fan ⇒ nWKL!
Proof
Definitions occuring in Statement :
nwkl!: nWKL!,
fan: Fan,
implies: P ⇒ Q
Definitions unfolded in proof :
implies: P ⇒ Q,
nwkl!: nWKL!,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
PFan: PFan{i:l}(),
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
not: ¬A,
false: False,
nat: ℕ,
pi1: fst(t),
pi2: snd(t),
top: Top,
infinite-tree: infinite-tree(A),
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
eff-unique: eff-unique(A),
cand: A c∧ B,
compose: f o g,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
int_iseg: {i...j},
bnot: ¬bb,
assert: ↑b,
squash: ↓T,
true: True,
is-path: is-path(A;f),
upto: upto(n),
from-upto: [n, m),
lt_int: i <z j,
nat_plus: ℕ+
Lemmas referenced :
fan-implies-PFan,
eff-unique_wf,
infinite-tree_wf,
list_wf,
bool_wf,
decidable_wf,
fan_wf,
not_wf,
map_wf,
pi1_wf,
subtype_rel_self,
pi2_wf,
decidable__not,
decidable__and2,
istype-void,
iseg_wf,
int_seg_wf,
upto_wf,
length_wf,
length-map,
istype-nat,
iseg-map,
decidable__exists_int_seg,
equal_wf,
int_seg_subtype_nat,
istype-false,
decidable__equal_bool,
list_extensionality,
map-length,
length_wf_nat,
istype-less_than,
subtype_rel_list,
top_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
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,
istype-le,
select-map,
length_upto,
select-upto,
subtype_rel_function,
nat_wf,
map-map,
imax_wf,
add_nat_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
imax_ub,
itermAdd_wf,
int_term_value_add_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_subtype,
le_weakening,
upto_iseg,
decidable__equal_list,
firstn_wf,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
select_wf,
btrue_wf,
subtype_base_sq,
list_subtype_base,
bool_subtype_base,
int_seg_properties,
length_firstn,
eqff_to_assert,
bool_cases_sqequal,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
select-firstn,
iseg_select,
set_subtype_base,
le_wf,
int_subtype_base,
monotone-upper-bound-function,
length_firstn_eq,
firstn-iseg,
firstn_firstn,
squash_wf,
true_wf,
iff_weakening_equal,
istype-universe,
trivial-equal,
is-path_wf,
ge_wf,
map_nil_lemma,
subtract-1-ge-0,
nil_wf,
first0,
upto_decomp1,
map_append_sq,
map_cons_lemma,
subtract-add-cancel,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
cons_wf,
append_wf,
firstn_decomp,
decidable__equal_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
Error :universeIsType,
dependent_functionElimination,
hypothesisEquality,
sqequalRule,
Error :functionIsType,
isectElimination,
applyEquality,
universeEquality,
rename,
Error :lambdaEquality_alt,
productEquality,
Error :productIsType,
Error :inhabitedIsType,
instantiate,
because_Cache,
Error :isect_memberEquality_alt,
voidElimination,
Error :equalityIstype,
natural_numberEquality,
setElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
independent_pairFormation,
promote_hyp,
independent_isectElimination,
unionElimination,
Error :dependent_set_memberEquality_alt,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
addEquality,
Error :inrFormation_alt,
Error :inlFormation_alt,
equalityElimination,
independent_pairEquality,
cumulativity,
Error :isect_memberFormation_alt,
intEquality,
sqequalBase,
functionExtensionality,
hyp_replacement,
imageElimination,
imageMemberEquality,
baseClosed,
intWeakElimination,
axiomSqEquality,
Error :functionIsTypeImplies,
closedConclusion
Latex:
Fan {}\mRightarrow{} nWKL!
Date html generated:
2019_06_20-PM-02_49_22
Last ObjectModification:
2018_12_07-PM-06_36_21
Theory : fan-theorem
Home
Index