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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