Nuprl Lemma : nat-retractible
retractible(ℕ)
Proof
Definitions occuring in Statement :
retractible: retractible(T),
nat: ℕ
Definitions unfolded in proof :
retractible: retractible(T),
exists: ∃x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
less_than: a < b,
less_than': less_than'(a;b),
top: Top,
true: True,
squash: ↓T,
not: ¬A,
false: False,
guard: {T},
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
has-value: (a)↓,
gt: i > j
Lemmas referenced :
nat_wf,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
has-value_wf_base,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
top_wf,
istype-void,
less_than_transitivity1,
less_than_irreflexivity,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
less_than_wf,
iff_weakening_uiff,
assert_of_bnot,
base_wf,
bottom_diverge,
not-gt-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :dependent_pairFormation_alt,
baseClosed,
sqequalRule,
Error :productIsType,
Error :functionIsType,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :equalityIsType4,
Error :inhabitedIsType,
hypothesisEquality,
baseApply,
closedConclusion,
applyEquality,
thin,
sqequalHypSubstitution,
isectElimination,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
independent_isectElimination,
because_Cache,
independent_pairFormation,
Error :lambdaFormation_alt,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
lessCases,
Error :isect_memberFormation_alt,
axiomSqEquality,
Error :isect_memberEquality_alt,
voidElimination,
imageMemberEquality,
imageElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
Error :equalityIsType1,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
callbyvalueLess,
Error :equalityIsType2,
Error :dependent_set_memberEquality_alt
Latex:
retractible(\mBbbN{})
Date html generated:
2019_06_20-AM-11_28_24
Last ObjectModification:
2018_09_29-PM-10_53_19
Theory : call!by!value_2
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