Nuprl Lemma : sqeq-copath5
∀[n,m:Top].  ((m + 1) - n - 1 ~ m - n - 1 - 1)
Proof
Definitions occuring in Statement : 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
subtract: n - m
, 
add: n + m
, 
natural_number: $n
, 
sqequal: s ~ t
Definitions unfolded in proof : 
not: ¬A
, 
is-exception: is-exception(t)
, 
false: False
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
top: Top
, 
subtype_rel: A ⊆r B
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
has-value: (a)↓
, 
subtract: n - m
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
exception-not-bottom, 
bottom_diverge, 
exception-not-value_1, 
int_subtype_base, 
sqle_wf_base, 
minus-minus, 
minus-add, 
zero-add, 
add-commutes, 
minus-one-mul-top, 
add-swap, 
minus-one-mul, 
base_wf, 
add-associates, 
add-is-int-iff, 
minus-is-int-iff, 
int-value-type, 
value-type-has-value, 
top_wf, 
is-exception_wf, 
has-value_wf_base
Rules used in proof : 
exceptionAdd, 
minusExceptionCases, 
sqleRule, 
independent_functionElimination, 
exceptionSqequal, 
axiomSqleEquality, 
addExceptionCases, 
applyLambdaEquality, 
hyp_replacement, 
sqleReflexivity, 
natural_numberEquality, 
minusEquality, 
voidEquality, 
voidElimination, 
lambdaEquality, 
applyEquality, 
addEquality, 
callbyvalueMinus, 
equalitySymmetry, 
equalityTransitivity, 
independent_isectElimination, 
intEquality, 
productElimination, 
callbyvalueAdd, 
because_Cache, 
isect_memberEquality, 
sqequalAxiom, 
hypothesis, 
hypothesisEquality, 
baseClosed, 
closedConclusion, 
baseApply, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
divergentSqle, 
sqequalSqle, 
thin, 
sqequalRule, 
cut, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[n,m:Top].    ((m  +  1)  -  n  -  1  \msim{}  m  -  n  -  1  -  1)
Date html generated:
2016_12_12-AM-09_16_29
Last ObjectModification:
2016_12_11-PM-05_22_46
Theory : co-recursion
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