Nuprl Lemma : radd-preserves-rless
∀x,y,z:ℝ. (x < y ⇐⇒ (z + x) < (z + y))
Proof
Definitions occuring in Statement :
rless: x < y,
radd: a + b,
real: ℝ,
all: ∀x:A. B[x],
iff: 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],
rev_implies: P ⇐ Q,
uimplies: b supposing a
Lemmas referenced :
rless_wf,
radd_wf,
real_wf,
rleq_weakening_equal,
radd_functionality_wrt_rless1,
rminus_wf,
radd_functionality_wrt_rless2,
int-to-real_wf,
rless_functionality,
req_inversion,
radd-assoc,
radd-ac,
radd_functionality,
radd-rminus-both,
req_weakening,
radd-zero-both
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality,
productElimination,
promote_hyp
Latex:
\mforall{}x,y,z:\mBbbR{}. (x < y \mLeftarrow{}{}\mRightarrow{} (z + x) < (z + y))
Date html generated:
2016_05_18-AM-07_06_44
Last ObjectModification:
2015_12_28-AM-00_37_25
Theory : reals
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