Nuprl Lemma : discontinuous_wf
∀[f:ℝ ⟶ ℝ]. ∀[x:ℝ]. (discontinuous(f;x) ∈ ℙ)
Proof
Definitions occuring in Statement :
discontinuous: discontinuous(f;x),
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,
discontinuous: discontinuous(f;x),
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
exists_wf,
real_wf,
rless_wf,
int-to-real_wf,
all_wf,
rabs_wf,
rsub_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
natural_numberEquality,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
because_Cache,
productEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[f:\mBbbR{} {}\mrightarrow{} \mBbbR{}]. \mforall{}[x:\mBbbR{}]. (discontinuous(f;x) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-11_13_42
Last ObjectModification:
2015_12_27-PM-10_39_12
Theory : reals
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