Nuprl Lemma : ds_property
∀[A:Type]. ∀[d:DS(A)]. ∀[a:A]. ∀[x,y:dstype(A; d; a)]. {uiff(x = y ∈ dstype(A; d; a);↑x = y)}
Proof
Definitions occuring in Statement :
eq_ds: x = y,
dstype: dstype(TypeNames; d; a),
discrete_struct: DS(A),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
guard: {T},
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
eq_ds: x = y,
dseq: dseq(d;a),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
discrete_struct: DS(A),
dstype: dstype(TypeNames; d; a),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
deq_property,
dstype_wf,
assert_witness,
discrete_struct_wf,
eq_ds_wf,
equal_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
productElimination,
independent_pairEquality,
because_Cache,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
universeEquality,
applyEquality
Latex:
\mforall{}[A:Type]. \mforall{}[d:DS(A)]. \mforall{}[a:A]. \mforall{}[x,y:dstype(A; d; a)]. \{uiff(x = y;\muparrow{}x = y)\}
Date html generated:
2016_05_14-PM-03_24_26
Last ObjectModification:
2015_12_26-PM-06_21_49
Theory : decidable!equality
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