Nuprl Lemma : add-nonneg
∀x,y:ℤ. (0 ≤ (x + y)) supposing ((0 ≤ x) and (0 ≤ y))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
le: A ≤ B,
all: ∀x:A. B[x],
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
prop: ℙ,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
le: A ≤ B
Lemmas referenced :
decidable__int_equal,
subtype_base_sq,
int_subtype_base,
less_than_wf,
add-zero,
equal_wf,
zero-add,
or_wf,
iff_weakening_uiff,
le_wf,
le-iff-less-or-equal,
less_than'_wf,
add-positive
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
isect_memberFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
hypothesis,
unionElimination,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
independent_functionElimination,
hypothesisEquality,
sqequalRule,
inrFormation,
natural_numberEquality,
addEquality,
inlFormation,
voidElimination,
addLevel,
introduction,
productElimination,
independent_pairEquality,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
isectEquality
Latex:
\mforall{}x,y:\mBbbZ{}. (0 \mleq{} (x + y)) supposing ((0 \mleq{} x) and (0 \mleq{} y))
Date html generated:
2016_05_13-PM-03_30_32
Last ObjectModification:
2015_12_26-AM-09_46_51
Theory : arithmetic
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