Nuprl Lemma : decidable__rat-interval-face
∀I,J:ℚInterval. Dec(I ≤ J)
Proof
Definitions occuring in Statement :
rat-interval-face: I ≤ J,
rational-interval: ℚInterval,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
rat-interval-face: I ≤ J,
rational-interval: ℚInterval,
all: ∀x:A. B[x]
Lemmas referenced :
decidable__equal_rational-interval,
qle_wf,
rat-point-interval_wf,
rational-interval_wf,
equal_wf,
decidable__or
Rules used in proof :
because_Cache,
dependent_functionElimination,
independent_functionElimination,
universeIsType,
inhabitedIsType,
setIsType,
dependent_pairEquality_alt,
rename,
setElimination,
unionEquality,
hypothesisEquality,
hypothesis,
isectElimination,
extract_by_obid,
introduction,
cut,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}I,J:\mBbbQ{}Interval. Dec(I \mleq{} J)
Date html generated:
2019_10_29-AM-07_47_14
Last ObjectModification:
2019_10_19-AM-10_34_48
Theory : rationals
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