Nuprl Lemma : mk-rset_wf
∀[P:ℝ ⟶ ℙ]. {x:ℝ | P[x]} ∈ Set(ℝ) supposing ∀x,y:ℝ. ((x = y) ⇒ P[x] ⇒ P[y])
Proof
Definitions occuring in Statement :
mk-rset: {x:ℝ | P[x]},
rset: Set(ℝ),
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
rset: Set(ℝ),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
mk-rset: {x:ℝ | P[x]},
so_apply: x[s],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
real_wf,
all_wf,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
lambdaEquality,
applyEquality,
hypothesisEquality,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[P:\mBbbR{} {}\mrightarrow{} \mBbbP{}]. \{x:\mBbbR{} | P[x]\} \mmember{} Set(\mBbbR{}) supposing \mforall{}x,y:\mBbbR{}. ((x = y) {}\mRightarrow{} P[x] {}\mRightarrow{} P[y])
Date html generated:
2016_05_18-AM-08_08_21
Last ObjectModification:
2015_12_28-AM-01_14_47
Theory : reals
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