Nuprl Lemma : lt_int_eq_true_elim_sqequal
∀[i,j:ℤ].  i < j supposing i <z j ~ tt
Proof
Definitions occuring in Statement : 
lt_int: i <z j
, 
btrue: tt
, 
less_than: a < b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
int: ℤ
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
true: True
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced : 
assert_of_lt_int, 
member-less_than, 
int_subtype_base
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
hypothesis, 
sqequalIntensionalEquality, 
sqequalRule, 
baseApply, 
closedConclusion, 
baseClosed, 
hypothesisEquality, 
applyEquality, 
thin, 
lemma_by_obid, 
sqequalHypSubstitution, 
because_Cache, 
isect_memberEquality, 
isectElimination, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
intEquality, 
natural_numberEquality, 
productElimination
Latex:
\mforall{}[i,j:\mBbbZ{}].    i  <  j  supposing  i  <z  j  \msim{}  tt
Date html generated:
2016_05_13-PM-04_10_33
Last ObjectModification:
2016_01_18-PM-05_39_38
Theory : subtype_1
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