Nuprl Lemma : test34
∀p:ℕ × ℕ. ∀bs:ℕ List. (let x,y = p in x + y ∈ ℤ)
Proof
Definitions occuring in Statement :
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
spread: spread def,
product: x:A × B[x],
add: n + m,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
list_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
spreadEquality,
hypothesisEquality,
addEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesis,
lemma_by_obid,
isectElimination,
productEquality
Latex:
\mforall{}p:\mBbbN{} \mtimes{} \mBbbN{}. \mforall{}bs:\mBbbN{} List. (let x,y = p in x + y \mmember{} \mBbbZ{})
Date html generated:
2016_05_15-PM-07_47_54
Last ObjectModification:
2015_12_27-AM-11_07_50
Theory : general
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