Nuprl Lemma : record+_wf
∀[T:𝕌']. ∀[B:T ⟶ 𝕌']. ∀[z:Atom]. (Tz:B[self] ∈ 𝕌')
Proof
Definitions occuring in Statement :
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],
member: t ∈ T,
record+: record+,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
so_apply: x[s],
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B
Lemmas referenced :
dep-isect_wf,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
functionEquality,
atomEquality,
isectElimination,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
applyEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
instantiate,
independent_functionElimination,
voidElimination,
universeEquality,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T:\mBbbU{}']. \mforall{}[B:T {}\mrightarrow{} \mBbbU{}']. \mforall{}[z:Atom]. (Tz:B[self] \mmember{} \mBbbU{}')
Date html generated:
2018_05_21-PM-08_38_18
Last ObjectModification:
2017_07_26-PM-06_02_38
Theory : general
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