Nuprl Lemma : identity-record-update
∀[T:Atom ⟶ 𝕌']. ∀[z:Atom]. ∀[r:record(x.T[x])]. (r[z := r.z] = r ∈ record(x.T[x]))
Proof
Definitions occuring in Statement :
record-update: r[x := v],
record-select: r.x,
record: record(x.T[x]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
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,
record: record(x.T[x]),
record-select: r.x,
record-update: r[x := v],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
guard: {T},
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
record_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
functionExtensionality,
sqequalRule,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
dependent_pairFormation,
promote_hyp,
because_Cache,
voidElimination,
lambdaEquality,
isect_memberEquality,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Atom {}\mrightarrow{} \mBbbU{}']. \mforall{}[z:Atom]. \mforall{}[r:record(x.T[x])]. (r[z := r.z] = r)
Date html generated:
2018_05_21-PM-08_40_16
Last ObjectModification:
2017_07_26-PM-06_04_23
Theory : general
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