Nuprl Lemma : rng_prod_1
∀[r:CRng]. ∀[n:ℕ]. ((Π(r) 0 ≤ i < n. 1) = 1 ∈ |r|)
Proof
Definitions occuring in Statement :
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T,
rng_prod: rng_prod,
crng: CRng,
rng_one: 1,
rng_car: |r|
Definitions unfolded in proof :
or: P ∨ Q,
decidable: Dec(P),
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
rng: Rng,
crng: CRng,
so_apply: x[s],
so_lambda: λ2x.t[x],
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
nat_plus: ℕ+,
squash: ↓T,
infix_ap: x f y
Lemmas referenced :
crng_wf,
nat_wf,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
rng_one_wf,
rng_prod_unroll_base,
rng_times_one,
rng_times_wf,
iff_weakening_equal,
int_seg_wf,
rng_prod_unroll_hi,
rng_car_wf,
true_wf,
squash_wf,
equal_wf
Rules used in proof :
unionElimination,
axiomEquality,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
intWeakElimination,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
because_Cache,
productElimination,
baseClosed,
imageMemberEquality,
dependent_set_memberEquality,
universeEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination,
applyEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[n:\mBbbN{}]. ((\mPi{}(r) 0 \mleq{} i < n. 1) = 1)
Date html generated:
2018_05_21-PM-09_33_25
Last ObjectModification:
2017_12_14-PM-07_06_09
Theory : matrices
Home
Index