Nuprl Lemma : div_fun_sat_div_nrel
∀[a:ℕ]. ∀[n:ℕ+]. Div(a;n;a ÷ n)
Proof
Definitions occuring in Statement :
div_nrel: Div(a;n;q),
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
divide: n ÷ m
Definitions unfolded in proof :
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
prop: ℙ,
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
nequal: a ≠ b ∈ T ,
nat_plus: ℕ+,
nat: ℕ,
false: False,
implies: P ⇒ Q,
not: ¬A,
le: A ≤ B,
and: P ∧ Q,
lelt: i ≤ j < k,
member: t ∈ T,
uall: ∀[x:A]. B[x],
div_nrel: Div(a;n;q),
less_than: a < b,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q
Lemmas referenced :
nat_wf,
nat_plus_wf,
false_wf,
int_formula_prop_le_lemma,
int_term_value_add_lemma,
int_term_value_mul_lemma,
intformle_wf,
itermAdd_wf,
itermMultiply_wf,
multiply-is-int-iff,
member-less_than,
int_subtype_base,
equal-wf-base,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
nat_plus_properties,
less_than'_wf,
rem_bounds_1,
div_rem_sum,
nat_plus_inc_int_nzero,
decidable__le,
istype-int,
istype-void,
add-is-int-iff,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__lt
Rules used in proof :
closedConclusion,
baseApply,
promote_hyp,
pointwiseFunctionality,
addEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
baseClosed,
applyEquality,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
divideEquality,
multiplyEquality,
hypothesis,
rename,
setElimination,
isectElimination,
extract_by_obid,
because_Cache,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality,
independent_pairEquality,
thin,
productElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution,
Error :lambdaFormation_alt,
imageElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
Error :universeIsType,
Error :equalityIstype,
Error :inhabitedIsType,
sqequalBase,
unionElimination
Latex:
\mforall{}[a:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. Div(a;n;a \mdiv{} n)
Date html generated:
2019_06_20-PM-01_14_17
Last ObjectModification:
2019_01_28-PM-03_17_33
Theory : int_2
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