Nuprl Lemma : le_int-wf-partial
∀[x,y:partial(Base)]. (x ≤z y ∈ partial(𝔹))
Proof
Definitions occuring in Statement :
partial: partial(T),
le_int: i ≤z j,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bool: 𝔹,
subtype_rel: A ⊆r B,
le_int: i ≤z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
not: ¬A,
squash: ↓T,
lt_int: i <z j,
false: False,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
less_than: a < b,
less_than': less_than'(a;b),
top: Top,
true: True,
has-value: (a)↓,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
assert: ↑b
Lemmas referenced :
base-member-partial,
bool_wf,
union-value-type,
unit_wf2,
partial-base,
has-value-bnot-type,
top_wf,
bfalse_wf,
btrue_wf,
equal_wf,
is-exception_wf,
partial_wf,
base_wf,
exception-not-value,
value-type-has-value,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
less_than_wf,
has-value_wf_base,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
partial-not-exception
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
lambdaFormation,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
decideExceptionCases,
imageElimination,
imageMemberEquality,
lessExceptionCases,
voidElimination,
equalityElimination,
productElimination,
lessCases,
axiomSqEquality,
independent_pairFormation,
voidEquality,
natural_numberEquality,
divergentSqle,
sqleReflexivity,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[x,y:partial(Base)]. (x \mleq{}z y \mmember{} partial(\mBbbB{}))
Date html generated:
2019_06_20-PM-00_34_21
Last ObjectModification:
2018_08_21-PM-01_53_29
Theory : partial_1
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