Nuprl Lemma : sbcode-mul
∀[m,n,k:ℕ+]. (sbcode(k * m;k * n) ~ sbcode(m;n))
Proof
Definitions occuring in Statement :
sbcode: sbcode(m;n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
multiply: n * m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
sbcode: sbcode(m;n),
sq_type: SQType(T),
less_than: a < b,
nat_plus: ℕ+,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
true: True,
squash: ↓T,
bfalse: ff,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
nat_plus_wf,
nat_wf,
int_seg_wf,
int_seg_properties,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
le_wf,
subtype_base_sq,
list_wf,
list_subtype_base,
set_subtype_base,
lelt_wf,
int_subtype_base,
decidable__lt,
itermAdd_wf,
int_term_value_add_lemma,
nat_plus_subtype_nat,
nat_plus_properties,
sbcode_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
top_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
cons_wf,
squash_wf,
true_wf,
itermMultiply_wf,
int_term_value_mul_lemma,
mul_preserves_le,
mul_preserves_lt,
nil_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
because_Cache,
productElimination,
unionElimination,
applyEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
instantiate,
cumulativity,
addEquality,
multiplyEquality,
equalityElimination,
lessCases,
imageMemberEquality,
baseClosed,
imageElimination,
promote_hyp,
universeEquality
Latex:
\mforall{}[m,n,k:\mBbbN{}\msupplus{}]. (sbcode(k * m;k * n) \msim{} sbcode(m;n))
Date html generated:
2018_05_21-PM-11_39_50
Last ObjectModification:
2017_07_26-PM-06_42_48
Theory : rationals
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