Nuprl Lemma : flip_inverse
∀[k:ℤ]. ∀[x,y:ℕk]. (((y, x) o (y, x)) = (λx.x) ∈ (ℕk ⟶ ℕk))
Proof
Definitions occuring in Statement :
flip: (i, j),
compose: f o g,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
flip: (i, j),
compose: f o g,
int_seg: {i..j-},
implies: P ⇒ Q,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
int_seg_wf,
eq_int_wf,
ifthenelse_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
equal_wf,
int_seg_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
bnot_wf,
not_wf,
lelt_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
and_wf,
eq_int_eq_true,
btrue_wf,
iff_weakening_equal,
uiff_transitivity,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
because_Cache,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
isect_memberEquality,
axiomEquality,
intEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
lambdaFormation,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
equalityElimination,
promote_hyp,
instantiate,
cumulativity,
applyLambdaEquality,
applyEquality,
imageElimination,
imageMemberEquality,
impliesFunctionality
Latex:
\mforall{}[k:\mBbbZ{}]. \mforall{}[x,y:\mBbbN{}k]. (((y, x) o (y, x)) = (\mlambda{}x.x))
Date html generated:
2017_04_17-AM-08_06_33
Last ObjectModification:
2017_02_27-PM-04_35_40
Theory : list_1
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