Nuprl Lemma : record_extensionality
∀[T:Atom ⟶ 𝕌']. ∀[r1,r2:record(x.T[x])]. uiff(r1 = r2 ∈ record(x.T[x]);∀a:Atom. (r1.a = r2.a ∈ T[a]))
Proof
Definitions occuring in Statement :
record-select: r.x,
record: record(x.T[x]),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
atom: Atom,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
record: record(x.T[x]),
record-select: r.x,
guard: {T}
Lemmas referenced :
and_wf,
equal_wf,
record_wf,
record-select_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
equalitySymmetry,
dependent_set_memberEquality,
hypothesis,
hypothesisEquality,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
lambdaEquality,
applyEquality,
atomEquality,
setElimination,
rename,
productElimination,
setEquality,
because_Cache,
dependent_functionElimination,
axiomEquality,
cumulativity,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
functionExtensionality
Latex:
\mforall{}[T:Atom {}\mrightarrow{} \mBbbU{}']. \mforall{}[r1,r2:record(x.T[x])]. uiff(r1 = r2;\mforall{}a:Atom. (r1.a = r2.a))
Date html generated:
2016_05_15-PM-06_40_43
Last ObjectModification:
2015_12_27-AM-11_52_11
Theory : general
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