Nuprl Lemma : fibs-equal-map
fibs() = stream-map(λn.fib(n);nats()) ∈ stream(ℕ)
Proof
Definitions occuring in Statement :
fibs: fibs(),
fib: fib(n),
nats: nats(),
stream-map: stream-map(f;s),
stream: stream(A),
nat: ℕ,
lambda: λx.A[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
label: ...$L... t,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
nat_wf,
nat_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__le,
fib_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
istype-le,
s-nth_wf,
fibs_wf,
nats_wf,
stream-subtype,
top_wf,
istype-nat,
equal_wf,
squash_wf,
true_wf,
istype-universe,
nth-fibs,
nth-stream-map,
nth-nats,
subtype_rel_self,
iff_weakening_equal,
stream-extensionality,
stream-map_wf
Rules used in proof :
because_Cache,
lambdaFormation,
independent_isectElimination,
hypothesisEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
lemma_by_obid,
cut,
introduction,
extract_by_obid,
setElimination,
rename,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
natural_numberEquality,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
Error :universeIsType,
Error :dependent_set_memberEquality_alt,
applyLambdaEquality,
applyEquality,
imageElimination,
Error :inhabitedIsType,
instantiate,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination
Latex:
fibs() = stream-map(\mlambda{}n.fib(n);nats())
Date html generated:
2019_06_20-PM-02_28_09
Last ObjectModification:
2019_01_15-PM-03_33_57
Theory : num_thy_1
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