Nuprl Lemma : flip-injection
∀[n:ℕ]. ∀[i,j:ℕn]. Inj(ℕn;ℕn;(i, j))
Proof
Definitions occuring in Statement :
flip: (i, j),
inject: Inj(A;B;f),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
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),
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
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,
ifthenelse: if b then t else f fi ,
bfalse: ff,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bnot: ¬bb,
btrue: tt,
assert: ↑b,
sq_type: SQType(T),
uiff: uiff(P;Q)
Lemmas referenced :
set_subtype_base,
lelt_wf,
istype-int,
int_subtype_base,
int_seg_wf,
istype-nat,
eq_int_wf,
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,
istype-le,
istype-less_than,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
istype-assert,
equal_wf,
squash_wf,
true_wf,
istype-universe,
bool_wf,
eq_int_eq_true,
btrue_wf,
subtype_rel_self,
iff_weakening_equal,
bfalse_wf,
bool_subtype_base,
assert_elim,
btrue_neq_bfalse,
subtype_rel-equal,
base_wf,
subtype_base_sq,
iff_imp_equal_bool,
iff_functionality_wrt_iff,
false_wf,
iff_weakening_uiff,
assert_of_eq_int,
ifthenelse_wf,
bool_cases,
eqtt_to_assert,
eqff_to_assert,
iff_transitivity,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
hypothesis,
Error :equalityIstype,
because_Cache,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
sqequalBase,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :universeIsType,
equalityTransitivity,
applyLambdaEquality,
productElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
voidElimination,
independent_pairFormation,
Error :dependent_set_memberEquality_alt,
Error :productIsType,
Error :functionIsType,
imageElimination,
instantiate,
universeEquality,
imageMemberEquality,
Error :equalityIsType4,
cumulativity
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[i,j:\mBbbN{}n]. Inj(\mBbbN{}n;\mBbbN{}n;(i, j))
Date html generated:
2019_06_20-PM-01_36_53
Last ObjectModification:
2018_11_24-AM-09_35_07
Theory : list_1
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