Nuprl Lemma : primrec-unroll+1
∀[n:{n:ℤ| 0 < n} ]. ∀[b,c:Top]. (primrec(n + 1;b;c) ~ c n primrec(n;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,
add: n + m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
less_than: a < b,
squash: ↓T,
cand: A c∧ B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtract: n - m,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
primrec-unroll-1,
decidable__lt,
istype-false,
not-lt-2,
less-iff-le,
condition-implies-le,
minus-add,
istype-void,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
istype-less_than,
add-subtract-cancel,
istype-top,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
independent_pairFormation,
imageElimination,
productElimination,
dependent_functionElimination,
unionElimination,
Error :lambdaFormation_alt,
voidElimination,
independent_functionElimination,
independent_isectElimination,
Error :isect_memberEquality_alt,
minusEquality,
because_Cache,
axiomSqEquality,
Error :inhabitedIsType,
Error :isectIsTypeImplies,
Error :setIsType
Latex:
\mforall{}[n:\{n:\mBbbZ{}| 0 < n\} ]. \mforall{}[b,c:Top]. (primrec(n + 1;b;c) \msim{} c n primrec(n;b;c))
Date html generated:
2019_06_20-AM-11_27_44
Last ObjectModification:
2019_05_08-PM-04_32_40
Theory : call!by!value_2
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