Nuprl Lemma : evalall-ifthenelse
∀[a,b,c:Top]. (evalall(if a then b else c fi ) ~ if a then evalall(b) else evalall(c) fi )
Proof
Definitions occuring in Statement :
evalall: evalall(t),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
evalall: evalall(t),
has-value: (a)↓,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff
Lemmas referenced :
assert_of_bnot,
eqff_to_assert,
is-exception_wf,
has-value_wf_base,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
top_wf,
isl_wf,
injection-eta,
has-value-ifthenelse-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
sqequalHypSubstitution,
sqequalRule,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
because_Cache,
unionElimination,
instantiate,
cumulativity,
independent_functionElimination,
productElimination,
sqleReflexivity,
baseApply,
closedConclusion,
baseClosed,
callbyvalueExceptionCases,
axiomSqleEquality,
decideExceptionCases,
exceptionSqequal,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[a,b,c:Top]. (evalall(if a then b else c fi ) \msim{} if a then evalall(b) else evalall(c) fi )
Date html generated:
2016_05_13-PM-04_07_46
Last ObjectModification:
2016_01_14-PM-07_46_15
Theory : fun_1
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