Nuprl Lemma : permutation-sign-id
∀[n:ℕ]. (permutation-sign(n;λx.x) ~ 1)
Proof
Definitions occuring in Statement :
permutation-sign: permutation-sign(n;f),
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
or: P ∨ Q,
decidable: Dec(P),
so_apply: x[s],
so_lambda: λ2x.t[x],
permutation-sign: permutation-sign(n;f),
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],
guard: {T},
sq_type: SQType(T),
true: True,
squash: ↓T,
int_seg: {i..j-},
less_than': less_than'(a;b),
le: A ≤ B,
subtype_rel: A ⊆r B,
lelt: i ≤ j < k,
assert: ↑b,
bnot: ¬bb,
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
sign: sign(x),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
nat_wf,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
int_prod0_lemma,
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,
int_subtype_base,
subtype_base_sq,
le_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
int_seg_wf,
true_wf,
squash_wf,
int-prod_wf,
false_wf,
int_seg_subtype_nat,
int_seg_properties,
assert-bnot,
bool_subtype_base,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
assert_of_le_int,
eqtt_to_assert,
bool_wf,
le_int_wf,
iff_weakening_equal,
int-prod-1
Rules used in proof :
unionElimination,
sqequalAxiom,
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,
equalitySymmetry,
equalityTransitivity,
cumulativity,
instantiate,
baseClosed,
imageMemberEquality,
dependent_set_memberEquality,
because_Cache,
functionEquality,
imageElimination,
applyEquality,
promote_hyp,
productElimination,
equalityElimination,
universeEquality,
sqequalIntensionalEquality
Latex:
\mforall{}[n:\mBbbN{}]. (permutation-sign(n;\mlambda{}x.x) \msim{} 1)
Date html generated:
2018_05_21-PM-00_57_55
Last ObjectModification:
2017_12_10-PM-01_34_59
Theory : num_thy_1
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