Nuprl Lemma : ispair-bool-if-co-list
∀[T:Type]. ∀[t:colist(T)]. (ispair(t) ∈ 𝔹)
Proof
Definitions occuring in Statement :
colist: colist(T),
bfalse: ff,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
ispair: if z is a pair then a otherwise b,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
or: P ∨ Q,
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
unit: Unit,
exists: ∃x:A. B[x],
ext-eq: A ≡ B
Lemmas referenced :
colist-ext,
istype-universe,
co-list-cases,
subtype_rel_b-union-left,
unit_wf2,
colist_wf,
unit_subtype_colist,
ext-eq_inversion,
b-union_wf,
subtype_rel_transitivity,
subtype_rel_weakening,
bfalse_wf,
subtype_rel_b-union-right,
btrue_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
universeEquality,
dependent_functionElimination,
unionElimination,
hypothesis_subsumption,
productEquality,
independent_isectElimination,
because_Cache,
productElimination,
equalityTransitivity,
equalitySymmetry,
equalityElimination,
sqequalRule,
axiomEquality,
universeIsType
Latex:
\mforall{}[T:Type]. \mforall{}[t:colist(T)]. (ispair(t) \mmember{} \mBbbB{})
Date html generated:
2019_10_16-AM-11_38_17
Last ObjectModification:
2019_06_26-PM-04_07_03
Theory : eval!all
Home
Index