Nuprl Lemma : radd-non-neg
∀x,y:ℝ. ((r0 ≤ x) ⇒ (r0 ≤ y) ⇒ (r0 ≤ (x + y)))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
radd: a + b,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
rleq_wf,
int-to-real_wf,
real_wf,
radd-preserves-rleq,
radd_wf,
rleq_transitivity,
rleq_functionality,
radd-zero,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
productElimination,
independent_isectElimination,
because_Cache
Latex:
\mforall{}x,y:\mBbbR{}. ((r0 \mleq{} x) {}\mRightarrow{} (r0 \mleq{} y) {}\mRightarrow{} (r0 \mleq{} (x + y)))
Date html generated:
2016_05_18-AM-07_10_05
Last ObjectModification:
2015_12_28-AM-00_38_38
Theory : reals
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