Nuprl Lemma : test4
∀p:ℕ × ℕ × 𝔹. ∀bs:ℕ List. (let x,y,ok = p in if ok then x + y else x - y fi ∈ ℤ)
Proof
Definitions occuring in Statement :
list: T List,
nat: ℕ,
ifthenelse: if b then t else f fi ,
bool: 𝔹,
spreadn: spread3,
all: ∀x:A. B[x],
member: t ∈ T,
product: x:A × B[x],
subtract: n - m,
add: n + m,
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
spreadn: spread3,
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z.t[x; y; z])
Lemmas referenced :
nat_wf,
bool_wf,
list_wf,
istype-universe,
ifthenelse_wf,
subtract_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
hypothesis,
intEquality,
because_Cache,
addEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
lambdaEquality_alt,
inhabitedIsType,
universeIsType,
isectElimination,
productIsType,
lambdaFormation_alt,
isect_memberFormation_alt,
productElimination,
sqequalRule,
applyEquality,
functionIsType,
universeEquality
Latex:
\mforall{}p:\mBbbN{} \mtimes{} \mBbbN{} \mtimes{} \mBbbB{}. \mforall{}bs:\mBbbN{} List. (let x,y,ok = p in if ok then x + y else x - y fi \mmember{} \mBbbZ{})
Date html generated:
2019_10_15-AM-11_36_15
Last ObjectModification:
2018_10_09-PM-00_01_31
Theory : general
Home
Index