Nuprl Lemma : not-new-name
∀[I:fset(ℕ)]. ∀x:names(I). ((x = new-name(I) ∈ ℤ) ⇒ False)
Proof
Definitions occuring in Statement :
new-name: new-name(I),
names: names(I),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
names: names(I),
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
squash: ↓T,
true: True
Lemmas referenced :
new-name-property,
equal_wf,
new-name_wf,
nat_wf,
not_wf,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
names_wf,
fset_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
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,
squash_wf,
true_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
intEquality,
applyEquality,
lambdaEquality,
setEquality,
independent_isectElimination,
because_Cache,
sqequalRule,
natural_numberEquality,
dependent_functionElimination,
voidElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
hyp_replacement,
equalitySymmetry,
imageElimination,
equalityTransitivity,
universeEquality,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}x:names(I). ((x = new-name(I)) {}\mRightarrow{} False)
Date html generated:
2018_05_23-AM-08_29_12
Last ObjectModification:
2017_12_02-PM-03_48_25
Theory : cubical!type!theory
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