Nuprl Lemma : typed-null-ite
∀[x,y:Top List]. ∀[b:𝔹]. null(if b then x else y fi ) = if b then null(x) else null(y) fi
Proof
Definitions occuring in Statement :
null: null(as),
list: T List,
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
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 ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
bool_wf,
eqtt_to_assert,
null_wf,
top_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
thin,
extract_by_obid,
hypothesis,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
sqequalRule,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[x,y:Top List]. \mforall{}[b:\mBbbB{}]. null(if b then x else y fi ) = if b then null(x) else null(y) fi
Date html generated:
2018_05_21-PM-06_36_50
Last ObjectModification:
2017_07_26-PM-04_52_52
Theory : general
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