Nuprl Lemma : rleq_functionality_wrt_implies
∀[a,b,c,d:ℝ]. ({a ≤ d supposing b ≤ c}) supposing ((c ≤ d) and (b ≥ a))
Proof
Definitions occuring in Statement :
rge: x ≥ y,
rleq: x ≤ y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T}
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rge: x ≥ y,
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
real: ℝ,
prop: ℙ
Lemmas referenced :
rleq_transitivity,
less_than'_wf,
rsub_wf,
real_wf,
nat_plus_wf,
rleq_wf,
rge_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
because_Cache,
applyEquality,
setElimination,
rename,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[a,b,c,d:\mBbbR{}]. (\{a \mleq{} d supposing b \mleq{} c\}) supposing ((c \mleq{} d) and (b \mgeq{} a))
Date html generated:
2016_05_18-AM-07_06_07
Last ObjectModification:
2015_12_28-AM-00_36_44
Theory : reals
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