Nuprl Lemma : mon_itop_txpose_invar
∀g:IAbMonoid. ∀n:ℕ. ∀E:ℕn ⟶ |g|. ∀x:ℕ+n. ((Π 0 ≤ j < n. E[txpose_perm(x;0).f j]) = (Π 0 ≤ j < n. E[j]) ∈ |g|)
Proof
Definitions occuring in Statement :
txpose_perm: txpose_perm,
perm_f: p.f,
int_seg: {i..j-},
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T,
mon_itop: Π lb ≤ i < ub. E[i],
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
txpose_perm: txpose_perm,
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
iabmonoid: IAbMonoid,
imon: IMonoid,
tswap: swap{n}(i;j),
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
infix_ap: x f y
Lemmas referenced :
int_seg_wf,
grp_car_wf,
nat_wf,
iabmonoid_wf,
int_seg_properties,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
tswap_wf,
lelt_wf,
false_wf,
equal_wf,
squash_wf,
true_wf,
mon_itop_split_el,
iff_weakening_equal,
grp_op_wf,
infix_ap_wf,
mon_itop_wf,
itermAdd_wf,
int_term_value_add_lemma,
mon_itop_unroll_lo,
tswap_eval_2,
imon_wf,
tswap_eval_3,
tswap_eval_1,
mon_assoc,
abmonoid_ac_1,
abmonoid_comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
functionEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
applyEquality,
functionExtensionality,
dependent_set_memberEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
addEquality
Latex:
\mforall{}g:IAbMonoid. \mforall{}n:\mBbbN{}. \mforall{}E:\mBbbN{}n {}\mrightarrow{} |g|. \mforall{}x:\mBbbN{}\msupplus{}n.
((\mPi{} 0 \mleq{} j < n. E[txpose\_perm(x;0).f j]) = (\mPi{} 0 \mleq{} j < n. E[j]))
Date html generated:
2017_10_01-AM-09_53_39
Last ObjectModification:
2017_03_03-PM-00_48_37
Theory : perms_1
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