Nuprl Lemma : strictness-remainder-left
∀[a:Top]. (⊥ rem a ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
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,
top: Top
Lemmas referenced :
value-type-has-value,
int-value-type,
equal_wf,
bottom_diverge,
exception-not-bottom,
bottom-sqle,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueRemainder,
sqequalHypSubstitution,
hypothesis,
baseClosed,
sqequalRule,
baseApply,
closedConclusion,
hypothesisEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
lambdaFormation,
extract_by_obid,
isectElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
remainderExceptionCases,
axiomSqleEquality,
because_Cache,
sqleReflexivity,
isect_memberEquality,
voidEquality,
sqequalAxiom
Latex:
\mforall{}[a:Top]. (\mbot{} rem a \msim{} \mbot{})
Date html generated:
2017_04_14-AM-07_21_40
Last ObjectModification:
2017_02_27-PM-02_54_59
Theory : computation
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