### 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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