Nuprl Lemma : rless*_functionality
∀a,b,c,d:ℝ*. (a = b ⇒ c = d ⇒ (a < c ⇐⇒ b < d))
Proof
Definitions occuring in Statement :
rless*: x < y,
req*: x = y,
real*: ℝ*,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rless*: x < y,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
rless*_wf,
req*_wf,
real*_wf,
rrel*_functionality,
rless_wf,
real_wf,
req_inversion,
rless_transitivity2,
rleq_weakening,
rless_transitivity1,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_functionElimination,
sqequalRule,
independent_isectElimination,
dependent_functionElimination,
because_Cache,
productElimination
Latex:
\mforall{}a,b,c,d:\mBbbR{}*. (a = b {}\mRightarrow{} c = d {}\mRightarrow{} (a < c \mLeftarrow{}{}\mRightarrow{} b < d))
Date html generated:
2018_05_22-PM-03_20_17
Last ObjectModification:
2017_10_06-PM-06_05_48
Theory : reals_2
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