Nuprl Lemma : qle-iff
∀a,b:ℚ. uiff(a ≤ b;a < b ∨ (a = b ∈ ℚ))
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
rationals: ℚ,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ,
guard: {T},
false: False
Lemmas referenced :
qless_trichot_qorder,
qless_complement_qorder,
rationals_wf,
qle_witness,
equal_wf,
qless_wf,
qless_transitivity_2_qorder,
qless_irreflexivity,
qle_wf,
qle_weakening_lt_qorder,
qle_weakening_eq_qorder,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
because_Cache,
hypothesis,
productElimination,
independent_pairFormation,
isect_memberFormation,
introduction,
independent_functionElimination,
rename,
unionElimination,
inlFormation,
sqequalRule,
inrFormation,
independent_isectElimination,
voidElimination
Latex:
\mforall{}a,b:\mBbbQ{}. uiff(a \mleq{} b;a < b \mvee{} (a = b))
Date html generated:
2016_05_15-PM-10_45_48
Last ObjectModification:
2015_12_27-PM-07_53_14
Theory : rationals
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