Nuprl Lemma : name_eq-normalize-name
∀[X,F,G:Top]. ∀[a,b:Name].
(case name_eq(a;b) ∧b X of inl(x) => F[x;a] | inr(x) => G[x] ~ case name_eq(a;b) ∧b X
of inl(x) =>
F[x;b]
| inr(x) =>
G[x])
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
name: Name,
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
name: Name,
sq_type: SQType(T),
guard: {T},
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Lemmas referenced :
name_eq_wf,
bool_wf,
eqtt_to_assert,
assert-name_eq,
subtype_base_sq,
name_wf,
list_subtype_base,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
top_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
because_Cache,
voidElimination,
isect_memberFormation,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[X,F,G:Top]. \mforall{}[a,b:Name].
(case name\_eq(a;b) \mwedge{}\msubb{} X of inl(x) => F[x;a] | inr(x) => G[x] \msim{} case name\_eq(a;b) \mwedge{}\msubb{} X
of inl(x) =>
F[x;b]
| inr(x) =>
G[x])
Date html generated:
2017_04_17-AM-09_17_20
Last ObjectModification:
2017_02_27-PM-05_21_46
Theory : decidable!equality
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