Nuprl Lemma : qdeq_wf
qdeq() ∈ EqDecider(ℚ)
Proof
Definitions occuring in Statement :
qdeq: qdeq(),
rationals: ℚ,
deq: EqDecider(T),
member: t ∈ T
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
deq: EqDecider(T),
member: t ∈ T,
qdeq: qdeq()
Lemmas referenced :
istype-assert,
assert-qeq,
rationals_wf,
qeq_wf2
Rules used in proof :
applyEquality,
productIsType,
functionIsType,
because_Cache,
equalityIstype,
independent_isectElimination,
productElimination,
independent_pairFormation,
lambdaFormation_alt,
sqequalRule,
universeIsType,
inhabitedIsType,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaEquality_alt,
dependent_set_memberEquality_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
qdeq() \mmember{} EqDecider(\mBbbQ{})
Date html generated:
2019_10_29-AM-07_43_24
Last ObjectModification:
2019_10_18-AM-11_45_20
Theory : rationals
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