Nuprl Lemma : qless_functionality_wrt_implies_1
∀[a,b,c,d:ℚ]. ({a < d supposing b < c}) supposing ((c ≤ d) and (b ≥ a))
Proof
Definitions occuring in Statement :
qge: a ≥ b,
qle: r ≤ s,
qless: r < s,
rationals: ℚ,
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,
qge: a ≥ b,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
qless_transitivity_1_qorder,
qless_transitivity_2_qorder,
qless_witness,
qless_wf,
qle_wf,
qge_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b,c,d:\mBbbQ{}]. (\{a < d supposing b < c\}) supposing ((c \mleq{} d) and (b \mgeq{} a))
Date html generated:
2016_05_15-PM-11_00_19
Last ObjectModification:
2015_12_27-PM-07_49_07
Theory : rationals
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