Nuprl Lemma : RankEx2_Prod?_wf
∀[S,T:Type]. ∀[v:RankEx2(S;T)]. (RankEx2_Prod?(v) ∈ 𝔹)
Proof
Definitions occuring in Statement :
RankEx2_Prod?: RankEx2_Prod?(v),
RankEx2: RankEx2(S;T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
RankEx2_LeafT: RankEx2_LeafT(leaft),
RankEx2_Prod?: RankEx2_Prod?(v),
pi1: fst(t),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
RankEx2_LeafS: RankEx2_LeafS(leafs),
RankEx2_Prod: RankEx2_Prod(prod),
RankEx2_Union: RankEx2_Union(union),
RankEx2_ListProd: RankEx2_ListProd(listprod),
RankEx2_UnionList: RankEx2_UnionList(unionlist)
Lemmas referenced :
RankEx2-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
bfalse_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
btrue_wf,
RankEx2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesis,
applyEquality,
sqequalRule,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
dependent_pairFormation,
voidElimination,
equalityEquality,
universeEquality
Latex:
\mforall{}[S,T:Type]. \mforall{}[v:RankEx2(S;T)]. (RankEx2\_Prod?(v) \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-09_01_14
Last ObjectModification:
2015_12_28-PM-06_51_07
Theory : C-semantics
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