Nuprl Lemma : equipollent-int_mod
∀m:ℕ+. ℤ_m ~ ℕm
Proof
Definitions occuring in Statement :
int_mod: ℤ_n,
equipollent: A ~ B,
int_seg: {i..j-},
nat_plus: ℕ+,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
int_mod: ℤ_n,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
implies: P ⇒ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
equipollent: A ~ B,
exists: ∃x:A. B[x],
biject: Bij(A;B;f),
inject: Inj(A;B;f),
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
surject: Surj(A;B;f),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
istype: istype(T),
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
less_than: a < b
Lemmas referenced :
nat_plus_wf,
int_mod_wf,
int_seg_wf,
mod_bounds,
equal_wf,
squash_wf,
true_wf,
istype-universe,
modulus_functionality_wrt_eqmod,
modulus_wf_int_mod,
int-subtype-int_mod,
subtype_rel_self,
iff_weakening_equal,
istype-le,
istype-less_than,
eqmod_wf,
istype-int,
biject_wf,
int_seg_subtype_nat,
istype-false,
set_subtype_base,
le_wf,
int_subtype_base,
eqmod_refl,
quotient-member-eq,
eqmod_equiv_rel,
modulus-equal-iff-eqmod,
int_seg_properties,
nat_plus_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
subtype_rel_set,
lelt_wf,
mod_bounds_1,
nat_plus_inc_int_nzero,
modulus_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
universeIsType,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
pointwiseFunctionalityForEquality,
natural_numberEquality,
sqequalRule,
pertypeElimination,
promote_hyp,
productElimination,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
independent_pairFormation,
dependent_set_memberEquality_alt,
applyEquality,
lambdaEquality_alt,
imageElimination,
instantiate,
universeEquality,
intEquality,
independent_isectElimination,
because_Cache,
imageMemberEquality,
baseClosed,
independent_functionElimination,
productIsType,
equalityIstype,
dependent_functionElimination,
sqequalBase,
dependent_pairFormation_alt,
pointwiseFunctionality,
applyLambdaEquality,
unionElimination,
approximateComputation,
int_eqEquality,
Error :memTop,
voidElimination
Latex:
\mforall{}m:\mBbbN{}\msupplus{}. \mBbbZ{}\_m \msim{} \mBbbN{}m
Date html generated:
2020_05_19-PM-10_03_14
Last ObjectModification:
2020_01_04-PM-08_03_22
Theory : num_thy_1
Home
Index