Nuprl Lemma : eq_ds_wf
∀[A:Type]. ∀[d:DS(A)]. ∀[a:A]. ∀[x,y:dstype(A; d; a)]. (x = y ∈ 𝔹)
Proof
Definitions occuring in Statement :
eq_ds: x = y,
dstype: dstype(TypeNames; d; a),
discrete_struct: DS(A),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
eq_ds: x = y,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
dseq_wf,
dstype_wf,
discrete_struct_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[d:DS(A)]. \mforall{}[a:A]. \mforall{}[x,y:dstype(A; d; a)]. (x = y \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_24_23
Last ObjectModification:
2015_12_26-PM-06_21_44
Theory : decidable!equality
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