Nuprl Lemma : record-select_wf2
∀[T:𝕌']. ∀[z:Atom]. ∀[B:T ⟶ 𝕌']. ∀[r:Tz:B[self]]. (r.z ∈ B[r])
Proof
Definitions occuring in Statement :
record-select: r.x,
record+: record+,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
record+: record+,
member: t ∈ T,
record-select: r.x,
subtype_rel: A ⊆r B,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
so_apply: x[s],
bfalse: ff,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
nequal: a ≠ b ∈ T ,
not: ¬A,
so_lambda: λ2x.t[x]
Lemmas referenced :
subtype_rel-equal,
eq_atom_wf,
top_wf,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
atom_subtype_base,
bool_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
assert-bnot,
neg_assert_of_eq_atom,
record+_wf,
istype-atom,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalHypSubstitution,
dependentIntersectionElimination,
cut,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
instantiate,
introduction,
extract_by_obid,
isectElimination,
because_Cache,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
sqequalRule,
cumulativity,
equalityIsType1,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
independent_isectElimination,
productElimination,
dependent_pairFormation_alt,
equalityIsType4,
baseApply,
closedConclusion,
baseClosed,
promote_hyp,
voidElimination,
universeIsType,
lambdaEquality_alt,
functionIsType,
universeEquality
Latex:
\mforall{}[T:\mBbbU{}']. \mforall{}[z:Atom]. \mforall{}[B:T {}\mrightarrow{} \mBbbU{}']. \mforall{}[r:Tz:B[self]]. (r.z \mmember{} B[r])
Date html generated:
2019_10_15-AM-11_28_40
Last ObjectModification:
2018_10_16-PM-02_35_40
Theory : general
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