Nuprl Lemma : null-ite
∀[b:𝔹]. ∀[x,y:Top]. (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),
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ 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,
prop: ℙ
Lemmas referenced :
top_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
baseClosed,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination
Latex:
\mforall{}[b:\mBbbB{}]. \mforall{}[x,y:Top]. (null(if b then x else y fi ) \msim{} if b then null(x) else null(y) fi )
Date html generated:
2018_05_21-PM-06_36_32
Last ObjectModification:
2017_07_26-PM-04_52_48
Theory : general
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