Nuprl Lemma : rev_permf_order_2
∀n:ℕ. ((rev_permf(n) o rev_permf(n)) = Id ∈ (ℕn ⟶ ℕn))
Proof
Definitions occuring in Statement :
rev_permf: rev_permf(n),
compose: f o g,
identity: Id,
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
identity: Id,
rev_permf: rev_permf(n),
compose: f o g,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
nat: ℕ,
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,
prop: ℙ
Lemmas referenced :
nat_wf,
int_seg_wf,
lelt_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformand_wf,
decidable__le,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
itermVar_wf,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
subtract_wf,
decidable__equal_int,
nat_properties,
int_seg_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
lambdaFormation,
cut,
functionExtensionality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
independent_pairFormation,
because_Cache
Latex:
\mforall{}n:\mBbbN{}. ((rev\_permf(n) o rev\_permf(n)) = Id)
Date html generated:
2016_05_16-AM-07_30_25
Last ObjectModification:
2016_01_16-PM-10_06_02
Theory : perms_1
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