Nuprl Lemma : subtype_rel-tag-case
∀[T1,T2:Type]. ∀[z:Atom]. z:T1 ⊆r z:T2 supposing T1 ⊆r T2
Proof
Definitions occuring in Statement :
tag-case: z:T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
tag-case: z:T,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
subtype_rel_product,
ifthenelse_wf,
eq_atom_wf,
top_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,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atomEquality,
lambdaEquality,
instantiate,
hypothesisEquality,
hypothesis,
universeEquality,
cumulativity,
because_Cache,
independent_isectElimination,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T1,T2:Type]. \mforall{}[z:Atom]. z:T1 \msubseteq{}r z:T2 supposing T1 \msubseteq{}r T2
Date html generated:
2018_05_21-PM-08_40_58
Last ObjectModification:
2017_07_26-PM-06_05_03
Theory : general
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