Nuprl Lemma : assert-int-deq
∀[x,y:ℤ].  uiff(↑(IntDeq x y);x = y ∈ ℤ)
Proof
Definitions occuring in Statement : 
int-deq: IntDeq
, 
assert: ↑b
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
apply: f a
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
int-deq: IntDeq
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
implies: P 
⇒ Q
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
deq: EqDecider(T)
Lemmas referenced : 
equal-wf-base, 
int_subtype_base, 
iff_weakening_uiff, 
assert_wf, 
eq_int_wf, 
assert_of_eq_int, 
assert_witness, 
uiff_wf, 
int-deq_wf, 
deq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
independent_pairFormation, 
hypothesis, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
intEquality, 
hypothesisEquality, 
applyEquality, 
because_Cache, 
addLevel, 
productElimination, 
independent_isectElimination, 
independent_functionElimination, 
cumulativity, 
instantiate, 
independent_pairEquality, 
isect_memberEquality, 
axiomEquality, 
lambdaEquality, 
setElimination, 
rename, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[x,y:\mBbbZ{}].    uiff(\muparrow{}(IntDeq  x  y);x  =  y)
Date html generated:
2019_06_20-PM-00_31_56
Last ObjectModification:
2018_08_24-PM-10_58_42
Theory : equality!deciders
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