Nuprl Lemma : extend_perm_over_txpose
∀n:ℕ. ∀i,j:ℕn. (↑{n}(txpose_perm(i;j)) = txpose_perm(i;j) ∈ Sym(n + 1))
Proof
Definitions occuring in Statement :
extend_perm: ↑{n}(p),
txpose_perm: txpose_perm,
sym_grp: Sym(n),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
sym_grp: Sym(n),
perm: Perm(T),
prop: ℙ,
txpose_perm: txpose_perm,
extend_perm: ↑{n}(p),
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
perm_b: p.b,
pi2: snd(t),
squash: ↓T,
true: True,
guard: {T},
int_seg: {i..j-},
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,
le: A ≤ B,
less_than: a < b
Lemmas referenced :
perm_sig_wf,
perm_properties,
lelt_wf,
decidable__lt,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
int_seg_properties,
txpose_perm_wf,
extend_permf_over_swap,
true_wf,
squash_wf,
mk_perm_wf,
perm_b_wf,
perm_f_wf,
inv_funs_wf,
nat_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
dependent_functionElimination,
equalitySymmetry,
sqequalRule,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
functionEquality,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
setEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j:\mBbbN{}n. (\muparrow{}\{n\}(txpose\_perm(i;j)) = txpose\_perm(i;j))
Date html generated:
2016_05_16-AM-07_31_31
Last ObjectModification:
2016_01_16-PM-10_05_57
Theory : perms_1
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