Nuprl Lemma : flip_bijection
∀k:ℕ. ∀i,j:ℕk. Bij(ℕk;ℕk;(i, j))
Proof
Definitions occuring in Statement :
flip: (i, j),
biject: Bij(A;B;f),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
biject: Bij(A;B;f),
surject: Surj(A;B;f),
inject: Inj(A;B;f),
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
uimplies: b supposing a,
flip: (i, j),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
guard: {T},
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
true: True
Lemmas referenced :
flip_wf,
set_subtype_base,
lelt_wf,
istype-int,
int_subtype_base,
int_seg_wf,
nat_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
int_seg_properties,
nat_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
istype-void,
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,
le_wf,
less_than_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
iff_imp_equal_bool,
bfalse_wf,
iff_functionality_wrt_iff,
assert_wf,
equal-wf-base,
false_wf,
iff_weakening_uiff,
iff_weakening_equal,
squash_wf,
true_wf,
equal_wf,
istype-universe,
eq_int_eq_true,
btrue_wf,
ifthenelse_wf,
assert_elim,
bnot_wf,
subtype_rel_self,
btrue_neq_bfalse
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
cut,
hypothesis,
Error :equalityIsType4,
Error :inhabitedIsType,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
independent_pairFormation,
Error :universeIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
applyLambdaEquality,
dependent_functionElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :dependent_set_memberEquality_alt,
Error :productIsType,
Error :equalityIsType2,
baseApply,
closedConclusion,
baseClosed,
promote_hyp,
instantiate,
cumulativity,
Error :equalityIsType1,
imageElimination,
imageMemberEquality,
universeEquality,
Error :equalityIsType3
Latex:
\mforall{}k:\mBbbN{}. \mforall{}i,j:\mBbbN{}k. Bij(\mBbbN{}k;\mBbbN{}k;(i, j))
Date html generated:
2019_06_20-PM-01_36_05
Last ObjectModification:
2018_10_05-PM-02_47_59
Theory : list_1
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