Nuprl Lemma : div_unique
∀[a:ℕ]. ∀[n:ℕ+]. ∀[p,q:ℕ]. (p = q ∈ ℤ) supposing (Div(a;n;q) and Div(a;n;p))
Proof
Definitions occuring in Statement :
div_nrel: Div(a;n;q),
nat_plus: ℕ+,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
ge: i ≥ j ,
nat: ℕ,
nat_plus: ℕ+,
and: P ∧ Q,
lelt: i ≤ j < k,
div_nrel: Div(a;n;q),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermConstant_wf,
itermAdd_wf,
intformless_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__equal_int,
nat_plus_properties,
nat_properties,
mul_cancel_in_lt,
lt_transitivity_2,
div_nrel_wf,
nat_wf,
nat_plus_wf
Rules used in proof :
independent_pairFormation,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
lambdaEquality_alt,
dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
unionElimination,
dependent_functionElimination,
independent_isectElimination,
natural_numberEquality,
addEquality,
rename,
setElimination,
multiplyEquality,
productElimination,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
inhabitedIsType
Latex:
\mforall{}[a:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[p,q:\mBbbN{}]. (p = q) supposing (Div(a;n;q) and Div(a;n;p))
Date html generated:
2019_10_15-AM-10_21_17
Last ObjectModification:
2019_09_21-AM-11_47_28
Theory : int_2
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