Nuprl Lemma : fibs_wf
fibs() ∈ stream(ℕ)
Proof
Definitions occuring in Statement :
fibs: fibs(),
stream: stream(A),
nat: ℕ,
member: t ∈ T
Definitions unfolded in proof :
fibs: fibs(),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
nat: ℕ,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
s-cons: x.s,
sq_type: SQType(T),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
s-tl: s-tl(s),
pi2: snd(t),
bnot: ¬bb,
assert: ↑b,
nat_plus: ℕ+,
subtract: n - m,
less_than: a < b,
squash: ↓T,
cand: A c∧ B,
stream: stream(A),
corec: corec(T.F[T])
Lemmas referenced :
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
istype-nat,
primrec-unroll,
lt_int_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
set_subtype_base,
le_wf,
int_subtype_base,
assert_wf,
less_than_wf,
eqtt_to_assert,
assert_of_lt_int,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
intformless_wf,
int_formula_prop_less_lemma,
not_wf,
istype-less_than,
istype-assert,
bool_cases,
subtype_base_sq,
bool_subtype_base,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
nat_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
stream-zip_wf2,
bool_cases_sqequal,
assert-bnot,
decidable__lt,
primrec1_lemma,
primrec0_lemma,
istype-top,
nat_plus_properties,
subtype_rel_wf,
primrec_wf,
top_wf,
istype-universe,
int_seg_wf,
primrec-wf-nat-plus,
add-subtract-cancel,
subtype_rel_product,
add-associates,
add-swap,
add-commutes,
zero-add,
ge_wf,
subtract-1-ge-0
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
Error :inhabitedIsType,
hypothesis,
Error :lambdaFormation_alt,
thin,
Error :equalityIstype,
hypothesisEquality,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
Error :lambdaEquality_alt,
Error :dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
introduction,
extract_by_obid,
isectElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :universeIsType,
because_Cache,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
productElimination,
independent_pairEquality,
Error :functionIsType,
instantiate,
cumulativity,
promote_hyp,
Error :productIsType,
universeEquality,
productEquality,
imageElimination,
intWeakElimination,
axiomEquality,
Error :functionIsTypeImplies
Latex:
fibs() \mmember{} stream(\mBbbN{})
Date html generated:
2019_06_20-PM-02_28_03
Last ObjectModification:
2019_03_13-PM-07_34_59
Theory : num_thy_1
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