Nuprl Lemma : nat-star-retract-id
∀[s:ℕ*]. (nat-star-retract(s) = s ∈ ℕ*)
Proof
Definitions occuring in Statement :
nat-star-retract: nat-star-retract(s),
nat-star: ℕ*,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat-star: ℕ*,
squash: ↓T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
nat-star-retract: nat-star-retract(s),
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
guard: {T},
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
decidable: Dec(P),
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
nat-star-retract_wf,
nat-star_wf,
all_wf,
nat_wf,
less_than_wf,
equal_wf,
bl-exists_wf,
int_seg_wf,
upto_wf,
l_member_wf,
lt_int_wf,
int_seg_subtype_nat,
false_wf,
bool_wf,
eqtt_to_assert,
assert-bl-exists,
l_exists_functionality,
assert_wf,
iff_weakening_uiff,
subtype_rel_set,
assert_of_lt_int,
set_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
l_exists_wf,
l_exists_iff,
decidable__lt,
int_seg_properties,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
intformnot_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_not_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyLambdaEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_set_memberEquality,
lambdaEquality,
functionEquality,
natural_numberEquality,
applyEquality,
functionExtensionality,
because_Cache,
intEquality,
lambdaFormation,
independent_isectElimination,
independent_pairFormation,
setEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination,
independent_functionElimination,
promote_hyp,
dependent_pairFormation,
instantiate,
cumulativity,
voidElimination,
int_eqEquality,
isect_memberEquality,
voidEquality,
computeAll
Latex:
\mforall{}[s:\mBbbN{}*]. (nat-star-retract(s) = s)
Date html generated:
2017_04_17-AM-09_55_14
Last ObjectModification:
2017_02_27-PM-05_49_38
Theory : continuity
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