Nuprl Lemma : mccarthy91-eq-91
∀x:ℤ. (mccarthy91(x) = if (x) < (102) then 91 else (x - 10) ∈ ℤ)
Proof
Definitions occuring in Statement :
mccarthy91: mccarthy91(x),
all: ∀x:A. B[x],
less: if (a) < (b) then c else d,
subtract: n - m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
less_than: a < b,
and: P ∧ Q,
less_than': less_than'(a;b),
uall: ∀[x:A]. B[x],
true: True,
squash: ↓T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
mccarthy91-sqeq,
top_wf,
less_than_wf,
subtract_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
natural_numberEquality,
lessCases,
independent_pairFormation,
isectElimination,
baseClosed,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
isect_memberFormation,
axiomSqEquality,
because_Cache,
imageElimination,
productElimination,
independent_functionElimination,
intEquality
Latex:
\mforall{}x:\mBbbZ{}. (mccarthy91(x) = if (x) < (102) then 91 else (x - 10))
Date html generated:
2019_06_20-PM-01_19_07
Last ObjectModification:
2018_08_20-PM-09_31_13
Theory : int_2
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