Nuprl Lemma : add-nat
∀[x,y:ℕ]. (x + y ∈ ℕ)
Proof
Definitions occuring in Statement :
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
add: n + m
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
sq_stable: SqStable(P),
squash: ↓T,
prop: ℙ
Lemmas referenced :
add_nat_wf,
nat_wf,
sq_stable__le,
equal_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
addEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
extract_by_obid,
isectElimination,
lambdaFormation,
natural_numberEquality,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x,y:\mBbbN{}]. (x + y \mmember{} \mBbbN{})
Date html generated:
2017_04_14-AM-07_20_37
Last ObjectModification:
2017_02_27-PM-02_54_22
Theory : arithmetic
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