Nuprl Lemma : assert_witness
∀[b:𝔹]. ((↑b) ⇒ (Ax ∈ ↑b))
Proof
Definitions occuring in Statement :
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
axiom: Ax
Definitions unfolded in proof :
assert: ↑b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
exposed-it: exposed-it,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False
Lemmas referenced :
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
ifthenelse_wf,
true_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesisEquality,
thin,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
axiomEquality,
natural_numberEquality,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
universeEquality,
lambdaEquality
Latex:
\mforall{}[b:\mBbbB{}]. ((\muparrow{}b) {}\mRightarrow{} (Ax \mmember{} \muparrow{}b))
Date html generated:
2019_06_20-AM-11_30_56
Last ObjectModification:
2018_08_01-AM-10_18_53
Theory : bool_1
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