Nuprl Lemma : dsdeq_wf
∀[A:Type]. ∀[d:DS(A)]. ∀[a:A]. (dsdeq(d;a) ∈ EqDecider(dstype(A; d; a)))
Proof
Definitions occuring in Statement :
dsdeq: dsdeq(d;a),
dstype: dstype(TypeNames; d; a),
discrete_struct: DS(A),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
dsdeq: dsdeq(d;a),
dstype: dstype(TypeNames; d; a),
discrete_struct: DS(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
pi2_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
productEquality
Latex:
\mforall{}[A:Type]. \mforall{}[d:DS(A)]. \mforall{}[a:A]. (dsdeq(d;a) \mmember{} EqDecider(dstype(A; d; a)))
Date html generated:
2016_05_14-PM-03_24_18
Last ObjectModification:
2015_12_26-PM-06_21_39
Theory : decidable!equality
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