Nuprl Lemma : decidable__dstype_equal
∀[A:Type]. ∀a:A. ∀d:DS(A). ∀x,y:dstype(A; d; a). Dec(x = y ∈ dstype(A; d; a))
Proof
Definitions occuring in Statement :
dstype: dstype(TypeNames; d; a),
discrete_struct: DS(A),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
dstype: dstype(TypeNames; d; a),
discrete_struct: DS(A),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
pi1: fst(t),
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
deq_wf,
decidable-equal-deq,
equal_wf,
pi1_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
productElimination,
thin,
sqequalHypSubstitution,
cut,
applyEquality,
functionExtensionality,
hypothesisEquality,
cumulativity,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
functionEquality,
universeEquality,
lambdaEquality,
dependent_pairEquality,
productEquality
Latex:
\mforall{}[A:Type]. \mforall{}a:A. \mforall{}d:DS(A). \mforall{}x,y:dstype(A; d; a). Dec(x = y)
Date html generated:
2017_04_17-AM-09_09_46
Last ObjectModification:
2017_02_27-PM-05_17_49
Theory : decidable!equality
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