Nuprl Lemma : nc-e-same
∀I:fset(ℕ). ∀z:ℕ. (e(z;z) = 1 ∈ I+z ⟶ I+z)
Proof
Definitions occuring in Statement :
nc-e: e(i;j),
add-name: I+i,
nh-id: 1,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
names-hom: I ⟶ J,
nh-id: 1,
nc-e: e(i;j),
member: t ∈ T,
uall: ∀[x:A]. B[x],
names: names(I),
nat: ℕ,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
squash: ↓T,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
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,
prop: ℙ,
label: ...$L... t,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
dM_inc_wf,
add-name_wf,
sq_stable__fset-member,
nat_wf,
int-deq_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
fset-member_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
iff_weakening_equal,
trivial-member-add-name1,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
names_wf,
istype-nat,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
functionExtensionality,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
because_Cache,
dependent_set_memberEquality_alt,
independent_functionElimination,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
natural_numberEquality,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
equalityIstype,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}I:fset(\mBbbN{}). \mforall{}z:\mBbbN{}. (e(z;z) = 1)
Date html generated:
2020_05_20-PM-01_37_04
Last ObjectModification:
2019_12_08-PM-07_04_49
Theory : cubical!type!theory
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