Nuprl Lemma : rpositive-rmax
∀x,y:ℝ. (rpositive(rmax(x;y)) ⇐⇒ rpositive(x) ∨ rpositive(y))
Proof
Definitions occuring in Statement :
rpositive: rpositive(x),
rmax: rmax(x;y),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
real: ℝ,
rev_implies: P ⇐ Q,
rpositive: rpositive(x),
sq_exists: ∃x:{A| B[x]},
rmax: rmax(x;y),
or: P ∨ Q,
guard: {T}
Lemmas referenced :
rpositive_wf,
rmax_wf,
real_wf,
or_wf,
imax_strict_ub,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
dependent_functionElimination,
natural_numberEquality,
productElimination,
independent_functionElimination,
unionElimination,
inlFormation,
dependent_set_memberFormation,
inrFormation,
introduction,
dependent_set_memberEquality,
because_Cache
Latex:
\mforall{}x,y:\mBbbR{}. (rpositive(rmax(x;y)) \mLeftarrow{}{}\mRightarrow{} rpositive(x) \mvee{} rpositive(y))
Date html generated:
2016_05_18-AM-07_01_02
Last ObjectModification:
2015_12_28-AM-00_33_34
Theory : reals
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