Nuprl Lemma : primrec-unroll-1
∀[n:{n:ℤ| 0 < n} ]. ∀[b,c:Top]. (primrec(n;b;c) ~ c (n - 1) primrec(n - 1;b;c))
Proof
Definitions occuring in Statement :
primrec: primrec(n;b;c),
less_than: a < b,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
apply: f a,
subtract: n - m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
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 ,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
not: ¬A,
less_than': less_than'(a;b),
true: True,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
primrec-unroll,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
less-iff-le,
add_functionality_wrt_le,
add-associates,
add-zero,
add-commutes,
le-add-cancel2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
less_than_wf,
iff_weakening_uiff,
assert_of_bnot,
top_wf,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_functionElimination,
addEquality,
applyEquality,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
intEquality,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
independent_pairFormation,
impliesFunctionality,
sqequalAxiom
Latex:
\mforall{}[n:\{n:\mBbbZ{}| 0 < n\} ]. \mforall{}[b,c:Top]. (primrec(n;b;c) \msim{} c (n - 1) primrec(n - 1;b;c))
Date html generated:
2018_05_21-PM-00_02_53
Last ObjectModification:
2018_05_19-AM-07_12_41
Theory : call!by!value_2
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