Nuprl Lemma : per-set-equality
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[a1,a2:A]. (a1 = a2 ∈ per-set(A;a.B[a])) supposing ((a1 = a2 ∈ A) and B[a1])
Proof
Definitions occuring in Statement :
per-set: per-set(A;a.B[a]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
per-set: per-set(A;a.B[a]),
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ
Lemmas referenced :
per-set_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
pointwiseFunctionalityForEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
pertypeMemberEquality,
equalityTransitivity,
independent_pairFormation,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[a1,a2:A]. (a1 = a2) supposing ((a1 = a2) and B[a1])
Date html generated:
2019_06_20-AM-11_30_24
Last ObjectModification:
2018_08_24-PM-01_04_02
Theory : per!type
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