Nuprl Lemma : fan-implies-PFan
Fan ⇒ PFan{i:l}()
Proof
Definitions occuring in Statement :
PFan: PFan{i:l}(),
fan: Fan,
implies: P ⇒ Q
Definitions unfolded in proof :
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
less_than': less_than'(a;b),
so_apply: x[s],
subtype_rel: A ⊆r B,
le: A ≤ B,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
lelt: i ≤ j < k,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
nat: ℕ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
fan: Fan,
all: ∀x:A. B[x],
PFan: PFan{i:l}(),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
pi1: fst(t),
pi2: snd(t),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
cand: A c∧ B,
squash: ↓T,
true: True,
less_than: a < b,
nat_plus: ℕ+,
nequal: a ≠ b ∈ T ,
int_nzero: ℤ-o
Lemmas referenced :
fan_wf,
decidable_wf,
iseg_wf,
false_wf,
int_seg_subtype_nat,
subtype_rel_function,
exists_wf,
pi2_wf,
upto_wf,
pi1_wf,
map_wf,
nat_wf,
decidable__equal_bool,
decidable__not,
decidable__implies,
decidable__all_int_seg,
decidable__and2,
subtype_rel_self,
unshuffle_wf,
list_wf,
int_term_value_add_lemma,
itermAdd_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermMultiply_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
select_wf,
equal_wf,
not_wf,
int_seg_wf,
all_wf,
bool_wf,
length_wf,
le_wf,
decidable__exists_int_seg,
select-upto,
select-map,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
bool_cases,
map-length,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
btrue_wf,
subtype_rel_list,
top_wf,
length_upto,
lelt_wf,
assert_wf,
bnot_wf,
imax_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
imax_ub,
iseg-map,
int_seg_subtype,
le_weakening,
upto_iseg,
map_length_nat,
iff_weakening_equal,
unshuffle-map,
true_wf,
squash_wf,
mul_bounds_1a,
length-shuffle,
shuffle_wf,
istype-false,
istype-int,
istype-void,
istype-nat,
length-map,
list_extensionality,
select-shuffle,
zero-add,
mul-commutes,
neg_assert_of_eq_int,
multiply-is-int-iff,
add-is-int-iff,
assert_of_eq_int,
eq_int_wf,
rem_invariant,
nequal_wf,
equal-wf-base,
int_subtype_base,
div_rem_sum,
div-cancel3,
div-cancel2,
rem_bounds_1,
list_subtype_base,
product_subtype_base,
divide_wf,
unshuffle-map'
Rules used in proof :
hypothesis,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
cumulativity,
equalitySymmetry,
equalityTransitivity,
dependent_set_memberEquality,
universeEquality,
instantiate,
functionExtensionality,
applyEquality,
addEquality,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
unionElimination,
productElimination,
independent_isectElimination,
functionEquality,
sqequalRule,
hypothesisEquality,
because_Cache,
rename,
setElimination,
natural_numberEquality,
multiplyEquality,
isectElimination,
productEquality,
lambdaEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
independent_pairEquality,
impliesFunctionality,
applyLambdaEquality,
equalityElimination,
promote_hyp,
inlFormation,
inrFormation,
imageElimination,
imageMemberEquality,
baseClosed,
Error :lambdaEquality_alt,
closedConclusion,
Error :lambdaFormation_alt,
Error :dependent_pairFormation_alt,
Error :isect_memberEquality_alt,
Error :universeIsType,
Error :inhabitedIsType,
hyp_replacement,
divideEquality,
baseApply,
pointwiseFunctionality,
remainderEquality,
addLevel
Latex:
Fan {}\mRightarrow{} PFan\{i:l\}()
Date html generated:
2019_06_20-PM-02_48_40
Last ObjectModification:
2019_01_11-PM-00_50_37
Theory : fan-theorem
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