### Nuprl Lemma : mk_deq_wf

`∀[T:Type]. ∀[p:∀x,y:T.  Dec(x = y ∈ T)].  (mk_deq(p) ∈ EqDecider(T))`

Proof

Definitions occuring in Statement :  mk_deq: `mk_deq(p)` deq: `EqDecider(T)` decidable: `Dec(P)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` member: `t ∈ T` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` mk_deq: `mk_deq(p)` deq: `EqDecider(T)` all: `∀x:A. B[x]` prop: `ℙ` implies: `P `` Q` decidable: `Dec(P)` or: `P ∨ Q` isl: `isl(x)` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` false: `False` not: `¬A` bfalse: `ff` true: `True` btrue: `tt` ifthenelse: `if b then t else f fi ` assert: `↑b` so_apply: `x[s]` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B`
Lemmas referenced :  istype-universe decidable_wf equal_wf assert_wf all_wf true_wf false_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalHypSubstitution hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry Error :functionIsType,  extract_by_obid isectElimination thin hypothesisEquality Error :inhabitedIsType,  Error :universeIsType,  Error :isect_memberEquality_alt,  universeEquality Error :dependent_set_memberEquality_alt,  Error :lambdaEquality_alt,  because_Cache Error :lambdaFormation_alt,  unionElimination Error :equalityIsType1,  dependent_functionElimination independent_functionElimination Error :productIsType,  applyEquality voidElimination natural_numberEquality independent_pairFormation lemma_by_obid lambdaEquality lambdaFormation

Latex:
\mforall{}[T:Type].  \mforall{}[p:\mforall{}x,y:T.    Dec(x  =  y)].    (mk\_deq(p)  \mmember{}  EqDecider(T))

Date html generated: 2019_06_20-PM-00_31_53
Last ObjectModification: 2018_10_06-AM-11_20_18

Theory : equality!deciders

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