Nuprl Lemma : req_rat_term_wf
∀[r:rat_term()]. ∀[p,q:int_term()]. (r ≡ p/q ∈ ℙ)
Proof
Definitions occuring in Statement :
req_rat_term: r ≡ p/q,
rat_term: rat_term(),
int_term: int_term(),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
req_rat_term: r ≡ p/q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
real_wf,
rat_term_to_real_wf,
rneq_wf,
real_term_value_wf,
int-to-real_wf,
req_wf,
uimplies_subtype,
rdiv_wf,
int_term_wf,
rat_term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
intEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
inhabitedIsType,
lambdaFormation_alt,
productElimination,
productEquality,
natural_numberEquality,
applyEquality,
independent_isectElimination,
because_Cache,
lambdaEquality_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[r:rat\_term()]. \mforall{}[p,q:int\_term()]. (r \mequiv{} p/q \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-09_40_51
Last ObjectModification:
2019_04_01-AM-10_51_36
Theory : reals
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