Nuprl Lemma : eq_int-wf-partial
∀[x,y:partial(Base)]. ((x =z y) ∈ partial(𝔹))
Proof
Definitions occuring in Statement :
partial: partial(T),
eq_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,
eq_int: (i =z j),
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
has-value: (a)↓,
and: P ∧ Q,
false: False,
squash: ↓T,
all: ∀x:A. B[x],
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
base-member-partial,
bool_wf,
union-value-type,
unit_wf2,
partial-base,
is-exception_wf,
partial_wf,
base_wf,
btrue_wf,
bfalse_wf,
exception-not-value,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
has-value_wf_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
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,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
isect_memberEquality,
callbyvalueIntEq,
productElimination,
int_eqEquality,
int_eqExceptionCases,
imageElimination,
imageMemberEquality,
voidElimination,
unionElimination,
equalityElimination,
int_eqReduceTrueSq,
divergentSqle,
sqleReflexivity,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
int_eqReduceFalseSq
Latex:
\mforall{}[x,y:partial(Base)]. ((x =\msubz{} y) \mmember{} partial(\mBbbB{}))
Date html generated:
2017_04_14-AM-07_40_43
Last ObjectModification:
2017_02_27-PM-03_12_48
Theory : partial_1
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