Nuprl Lemma : qle_connex
∀a,b:ℚ. ((a ≤ b) ∨ (b ≤ a))
Proof
Definitions occuring in Statement :
qle: r ≤ s,
rationals: ℚ,
all: ∀x:A. B[x],
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a
Lemmas referenced :
qless_trichot_qorder,
qle_wf,
rationals_wf,
qle_weakening_lt_qorder,
qle_weakening_eq_qorder
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
unionElimination,
inlFormation,
isectElimination,
hypothesis,
sqequalRule,
inrFormation,
independent_isectElimination,
equalitySymmetry
Latex:
\mforall{}a,b:\mBbbQ{}. ((a \mleq{} b) \mvee{} (b \mleq{} a))
Date html generated:
2016_05_15-PM-11_02_13
Last ObjectModification:
2015_12_27-PM-07_47_57
Theory : rationals
Home
Index