Nuprl Lemma : dseq_wf
∀[TypeNames:Type]. ∀[d:DS(TypeNames)]. ∀[a:TypeNames].
(dseq(d;a) ∈ dstype(TypeNames; d; a) ⟶ dstype(TypeNames; d; a) ⟶ 𝔹)
Proof
Definitions occuring in Statement :
dseq: dseq(d;a),
dstype: dstype(TypeNames; d; a),
discrete_struct: DS(A),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
discrete_struct: DS(A),
dseq: dseq(d;a),
dstype: dstype(TypeNames; d; a),
pi1: fst(t),
pi2: snd(t),
subtype_rel: A ⊆r B,
deq: EqDecider(T)
Lemmas referenced :
deq_wf,
discrete_struct_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
applyEquality,
hypothesisEquality,
lambdaEquality,
setElimination,
rename,
lemma_by_obid,
isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[TypeNames:Type]. \mforall{}[d:DS(TypeNames)]. \mforall{}[a:TypeNames].
(dseq(d;a) \mmember{} dstype(TypeNames; d; a) {}\mrightarrow{} dstype(TypeNames; d; a) {}\mrightarrow{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_24_21
Last ObjectModification:
2015_12_26-PM-06_21_42
Theory : decidable!equality
Home
Index