Nuprl Lemma : assert-exception-name
∀[n:Atom2]. ∀[t:Value() ⋃ Exception(n;Top)].
(t ∈ Exception(n;Top) supposing ↑exception-name(t;n) ∧ t ∈ Value() supposing ¬↑exception-name(t;n))
Proof
Definitions occuring in Statement :
exception-name: exception-name(e;n),
Value: Value(),
Exception: Exception(n;T),
atom: Atom$n,
b-union: A ⋃ B,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
and: P ∧ Q,
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
pi2: snd(t),
ifthenelse: if b then t else f fi ,
unit: Unit,
bool: 𝔹,
tunion: ⋃x:A.B[x],
b-union: A ⋃ B,
uimplies: b supposing a,
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
false: False,
exception-name: exception-name(e;n),
Value: Value(),
has-value: (a)↓,
bfalse: ff,
assert: ↑b,
btrue: tt,
band: p ∧b q,
or: P ∨ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
not: ¬A,
Exception: Exception(n;T),
exception-with-name: exception-with-name(n;t),
subtype_rel: A ⊆r B,
true: True,
guard: {T},
sq_type: SQType(T),
mono: mono(T),
exists: ∃x:A. B[x],
is-above: is-above(T;a;z)
Lemmas referenced :
equal-wf-base,
sqle_wf_base,
bool-mono,
band_wf,
btrue_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
has-value_wf_base,
is-exception_wf,
atom2_subtype_base,
has-value-implies-dec-isaxiom-2,
assert_wf,
exception-name_wf,
not_wf,
b-union_wf,
Value_wf,
Exception_wf,
top_wf
Rules used in proof :
atomnEquality,
because_Cache,
isect_memberEquality,
independent_pairEquality,
independent_pairFormation,
isectElimination,
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
sqequalRule,
equalityElimination,
unionElimination,
thin,
productElimination,
imageElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
voidElimination,
setElimination,
rename,
tryReduceValue,
atomn_eqReduceTrueSq,
baseClosed,
independent_functionElimination,
dependent_functionElimination,
closedConclusion,
baseApply,
applyEquality,
sqleReflexivity,
sqleRule,
divergentSqle,
natural_numberEquality,
isintReduceTrue,
independent_isectElimination,
cumulativity,
instantiate,
productEquality,
dependent_pairFormation
Latex:
\mforall{}[n:Atom2]. \mforall{}[t:Value() \mcup{} Exception(n;Top)].
(t \mmember{} Exception(n;Top) supposing \muparrow{}exception-name(t;n)
\mwedge{} t \mmember{} Value() supposing \mneg{}\muparrow{}exception-name(t;n))
Date html generated:
2019_06_20-PM-00_28_37
Last ObjectModification:
2018_10_15-PM-02_27_53
Theory : subtype_1
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