Nuprl Lemma : round-robin-equal
∀[L:Top List]. ∀[b:ℕ]. (round-robin(L) (b + ||L||) ~ round-robin(L) b) supposing 0 < ||L||
Proof
Definitions occuring in Statement :
round-robin: round-robin(L),
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
round-robin: round-robin(L),
squash: ↓T,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
nat_plus: ℕ+,
nequal: a ≠ b ∈ T ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T)
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
rem_rec_case,
length_wf,
top_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
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_less_lemma,
int_formula_prop_wf,
le_wf,
less_than_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
equal-wf-T-base,
iff_weakening_equal,
add-subtract-cancel,
nat_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
productElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
remainderEquality,
lambdaFormation,
baseClosed,
imageMemberEquality,
independent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[L:Top List]. \mforall{}[b:\mBbbN{}]. (round-robin(L) (b + ||L||) \msim{} round-robin(L) b) supposing 0 < ||L||
Date html generated:
2017_04_17-AM-09_15_26
Last ObjectModification:
2017_02_27-PM-05_21_08
Theory : decidable!equality
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