Nuprl Lemma : equal-zero-streams
fix((λx.<⋅, x>)) ~ fix((λx.<⋅, ⋅, x>))
Proof
Definitions occuring in Statement :
it: ⋅,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
compose: f o g,
sq_stable: SqStable(P),
squash: ↓T,
nat_plus: ℕ+
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__int_equal,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
lelt_wf,
subtype_rel_self,
int_seg_properties,
le_wf,
fun_exp0_lemma,
bottom-sqle,
fun_exp1_lemma,
bottom_diverge,
exception-not-bottom,
has-value_wf_base,
is-exception_wf,
decidable__lt,
not-lt-2,
not-equal-2,
le-add-cancel-alt,
nat_wf,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
fun_exp_unroll_1,
minus-zero,
le-add-cancel2
Rules used in proof :
sqequalSqle,
fixpointLeast,
cut,
thin,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
axiomSqleEquality,
productElimination,
unionElimination,
independent_pairFormation,
addEquality,
applyEquality,
isect_memberEquality,
voidEquality,
intEquality,
minusEquality,
because_Cache,
instantiate,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis_subsumption,
cumulativity,
divergentSqle,
sqleRule,
sqleReflexivity,
baseClosed,
imageMemberEquality,
imageElimination,
multiplyEquality,
baseApply,
closedConclusion
Latex:
fix((\mlambda{}x.<\mcdot{}, x>)) \msim{} fix((\mlambda{}x.<\mcdot{}, \mcdot{}, x>))
Date html generated:
2018_05_21-PM-00_05_44
Last ObjectModification:
2018_05_19-AM-07_01_40
Theory : co-recursion
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