Nuprl Lemma : rrel*_wf
∀[R:ℝ ⟶ ℝ ⟶ ℙ]. ∀[x,y:ℝ*]. (R*(x,y) ∈ ℙ)
Proof
Definitions occuring in Statement :
rrel*: R*(x,y),
real*: ℝ*,
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rrel*: R*(x,y),
so_lambda: λ2x.t[x],
nat: ℕ,
real*: ℝ*,
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
exists_wf,
nat_wf,
all_wf,
int_upper_wf,
real_wf,
int_upper_subtype_nat,
real*_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
because_Cache,
applyEquality,
functionExtensionality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[R:\mBbbR{} {}\mrightarrow{} \mBbbR{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[x,y:\mBbbR{}*]. (R*(x,y) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-03_13_57
Last ObjectModification:
2017_10_06-PM-02_48_47
Theory : reals_2
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