Nuprl Lemma : RankEx2_Union_wf
∀[S,T:Type]. ∀[union:S × RankEx2(S;T) + RankEx2(S;T)]. (RankEx2_Union(union) ∈ RankEx2(S;T))
Proof
Definitions occuring in Statement :
RankEx2_Union: RankEx2_Union(union),
RankEx2: RankEx2(S;T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
RankEx2: RankEx2(S;T),
RankEx2_Union: RankEx2_Union(union),
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
ext-eq: A ≡ B,
RankEx2co_size: RankEx2co_size(p),
RankEx2_size: RankEx2_size(p),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A
Lemmas referenced :
RankEx2co-ext,
subtype_rel_union,
RankEx2_wf,
RankEx2co_wf,
subtype_rel_product,
eq_atom_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
eqtt_to_assert,
assert_of_eq_atom,
list_wf,
add_nat_wf,
false_wf,
le_wf,
RankEx2_size_wf,
pi2_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
has-value_wf-partial,
RankEx2co_size_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
dependent_pairEquality,
tokenEquality,
applyEquality,
productEquality,
independent_isectElimination,
lambdaEquality,
because_Cache,
lambdaFormation,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
unionEquality,
voidEquality,
equalityEquality,
natural_numberEquality,
independent_pairFormation,
intEquality,
universeEquality
Latex:
\mforall{}[S,T:Type]. \mforall{}[union:S \mtimes{} RankEx2(S;T) + RankEx2(S;T)]. (RankEx2\_Union(union) \mmember{} RankEx2(S;T))
Date html generated:
2016_05_16-AM-09_00_14
Last ObjectModification:
2015_12_28-PM-06_52_10
Theory : C-semantics
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