Nuprl Lemma : str1-to-nat_wf
∀[a:Atom]. (str1-to-nat(a) ∈ ℕ)
Proof
Definitions occuring in Statement :
str1-to-nat: str1-to-nat(a),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom
Definitions unfolded in proof :
str1-to-nat: str1-to-nat(a),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
false_wf,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
tokenEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
axiomEquality,
atomEquality
Latex:
\mforall{}[a:Atom]. (str1-to-nat(a) \mmember{} \mBbbN{})
Date html generated:
2017_04_17-AM-09_17_56
Last ObjectModification:
2017_02_27-PM-05_22_10
Theory : decidable!equality
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