Nuprl Lemma : mk_dset_wf
∀[T:Type]. ∀[eq:T ⟶ T ⟶ 𝔹]. mk_dset(T, eq) ∈ DSet supposing IsEqFun(T;eq)
Proof
Definitions occuring in Statement :
mk_dset: mk_dset(T, eq),
dset: DSet,
eqfun_p: IsEqFun(T;eq),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
mk_dset: mk_dset(T, eq),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
dset: DSet,
poset_sig: PosetSig,
set_car: |p|,
pi1: fst(t),
set_eq: =b,
pi2: snd(t),
prop: ℙ
Lemmas referenced :
bool_wf,
eqfun_p_wf,
set_car_wf,
set_eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
dependent_pairEquality,
hypothesisEquality,
functionEquality,
lemma_by_obid,
hypothesis,
productEquality,
sqequalHypSubstitution,
isectElimination,
thin,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. mk\_dset(T, eq) \mmember{} DSet supposing IsEqFun(T;eq)
Date html generated:
2016_05_15-PM-00_04_07
Last ObjectModification:
2015_12_26-PM-11_28_57
Theory : sets_1
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