Nuprl Lemma : two-factorizations-no-repeats
∀[n:ℕ]. no_repeats(ℤ × ℤ;two-factorizations(n))
Proof
Definitions occuring in Statement :
two-factorizations: two-factorizations(n),
no_repeats: no_repeats(T;l),
nat: ℕ,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
two-factorizations: two-factorizations(n),
mapfilter: mapfilter(f;P;L),
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
guard: {T},
inject: Inj(A;B;f),
sq_stable: SqStable(P),
squash: ↓T,
cand: A c∧ B,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
pi1: fst(t),
less_than: a < b
Lemmas referenced :
top_wf,
subtype_rel_product,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
decidable__lt,
int_formula_prop_not_lemma,
intformnot_wf,
decidable__le,
squash_wf,
member-less_than,
sq_stable__less_than,
sq_stable__le,
sq_stable__and,
decidable__equal_int,
decidable__equal_set,
sq_stable__l_member,
no_repeats-subtype,
no_repeats_from-upto,
no_repeats_filter,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
eq_int_wf,
set_wf,
l_member_wf,
from-upto_wf,
filter_wf5,
less_than_wf,
no_repeats_map,
nat_wf,
pi2_wf,
equal_wf,
pi1_wf_top,
le_wf,
and_wf,
subtype_rel_list,
two-factorizations_wf,
no_repeats_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
intEquality,
hypothesisEquality,
hypothesis,
applyEquality,
setEquality,
natural_numberEquality,
because_Cache,
sqequalRule,
setElimination,
rename,
multiplyEquality,
lambdaEquality,
independent_isectElimination,
independent_functionElimination,
addEquality,
lambdaFormation,
remainderEquality,
productElimination,
dependent_pairFormation,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
independent_pairEquality,
divideEquality,
imageMemberEquality,
baseClosed,
imageElimination,
unionElimination,
equalitySymmetry,
equalityTransitivity
Latex:
\mforall{}[n:\mBbbN{}]. no\_repeats(\mBbbZ{} \mtimes{} \mBbbZ{};two-factorizations(n))
Date html generated:
2016_05_15-PM-07_53_29
Last ObjectModification:
2016_01_16-AM-09_52_26
Theory : general
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