Nuprl Lemma : eqff_to_assert
∀[b:𝔹]. uiff(b = ff;↑¬bb)
Proof
Definitions occuring in Statement :
bnot: ¬bb,
assert: ↑b,
bfalse: ff,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
true: True,
prop: ℙ,
false: False,
sq_type: SQType(T),
guard: {T},
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
bnot_wf,
bool_wf,
true_wf,
false_wf,
equal_wf,
equal-wf-T-base,
assert_wf,
subtype_base_sq,
bool_subtype_base,
bfalse_wf,
iff_weakening_uiff,
sqequal-wf-base,
sqeqff_to_assert,
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
isect_memberEquality,
isectElimination,
hypothesisEquality,
extract_by_obid,
hypothesis,
lambdaFormation,
unionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
dependent_functionElimination,
independent_functionElimination,
baseClosed,
independent_pairFormation,
instantiate,
cumulativity,
independent_isectElimination,
sqequalAxiom,
sqequalIntensionalEquality,
applyEquality,
addLevel,
because_Cache
Latex:
\mforall{}[b:\mBbbB{}]. uiff(b = ff;\muparrow{}\mneg{}\msubb{}b)
Date html generated:
2017_04_14-AM-07_14_17
Last ObjectModification:
2017_02_27-PM-02_50_05
Theory : union
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