### Nuprl Lemma : rem-minus-1

`∀a:ℤ. (a rem -1 ~ 0)`

Proof

Definitions occuring in Statement :  all: `∀x:A. B[x]` remainder: `n rem m` minus: `-n` natural_number: `\$n` int: `ℤ` sqequal: `s ~ t`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` int_nzero: `ℤ-o` true: `True` nequal: `a ≠ b ∈ T ` not: `¬A` implies: `P `` Q` sq_type: `SQType(T)` guard: `{T}` false: `False` prop: `ℙ` absval: `|i|` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` less_than: `a < b` less_than': `less_than'(a;b)` squash: `↓T` cand: `A c∧ B` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` le: `A ≤ B` subtract: `n - m` bfalse: `ff` exists: `∃x:A. B[x]` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation_alt cut thin instantiate introduction extract_by_obid sqequalHypSubstitution isectElimination cumulativity intEquality independent_isectElimination hypothesis dependent_functionElimination dependent_set_memberEquality_alt minusEquality natural_numberEquality equalityTransitivity equalitySymmetry independent_functionElimination voidElimination equalityIstype inhabitedIsType hypothesisEquality baseClosed sqequalBase universeIsType because_Cache sqequalRule unionElimination equalityElimination productElimination lessCases isect_memberFormation_alt axiomSqEquality isect_memberEquality_alt isectIsTypeImplies independent_pairFormation Error :memTop,  imageMemberEquality imageElimination addEquality dependent_pairFormation_alt promote_hyp functionIsType multiplyEquality

Latex:
\mforall{}a:\mBbbZ{}.  (a  rem  -1  \msim{}  0)

Date html generated: 2020_05_19-PM-09_35_28
Last ObjectModification: 2019_12_26-PM-09_50_46

Theory : arithmetic

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