Nuprl Lemma : strictness-remainder-right
∀[a:Top]. (a rem ⊥ ~ eval u = a in ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
callbyvalue: callbyvalue,
uall: ∀[x:A]. B[x],
top: Top,
remainder: n rem m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
not: ¬A,
false: False
Lemmas referenced :
value-type-has-value,
int-value-type,
equal_wf,
bottom_diverge,
exception-not-bottom,
has-value_wf_base,
is-exception_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueRemainder,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
lambdaFormation,
extract_by_obid,
isectElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
remainderExceptionCases,
axiomSqleEquality,
exceptionSqequal,
sqleReflexivity,
because_Cache,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases,
sqequalAxiom
Latex:
\mforall{}[a:Top]. (a rem \mbot{} \msim{} eval u = a in \mbot{})
Date html generated:
2017_04_14-AM-07_21_43
Last ObjectModification:
2017_02_27-PM-02_55_09
Theory : computation
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