Nuprl Lemma : equal-bnot
∀[x,y:𝔹]. uiff(x = ¬by;¬x = y)
Proof
Definitions occuring in Statement :
bnot: ¬bb,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
not: ¬A,
false: False,
prop: ℙ,
assert: ↑b,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
decidable: Dec(P)
Lemmas referenced :
eqtt_to_assert,
btrue_neq_bfalse,
equal-wf-T-base,
bool_wf,
iff_imp_equal_bool,
bfalse_wf,
assert_elim,
assert_wf,
false_wf,
not_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert_witness,
assert_of_bnot,
bnot_wf,
uiff_wf,
iff_weakening_uiff,
decidable__assert
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
hypothesisEquality,
thin,
because_Cache,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
independent_pairFormation,
isect_memberFormation,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
baseClosed,
lambdaEquality,
dependent_functionElimination,
addLevel,
levelHypothesis,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
functionEquality,
independent_pairEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[x,y:\mBbbB{}]. uiff(x = \mneg{}\msubb{}y;\mneg{}x = y)
Date html generated:
2017_10_01-AM-09_12_43
Last ObjectModification:
2017_07_26-PM-04_48_20
Theory : general
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