Nuprl Lemma : rel-connected_weakening
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[x,y:T].  x──R⟶y supposing x = y ∈ T
Proof
Definitions occuring in Statement : 
rel-connected: x──R⟶y
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
rel-connected: x──R⟶y
, 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
rel_star: R^*
, 
infix_ap: x f y
, 
exists: ∃x:A. B[x]
, 
nat: ℕ
, 
le: A ≤ B
, 
and: P ∧ Q
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
rel_exp: R^n
, 
ifthenelse: if b then t else f fi 
, 
eq_int: (i =z j)
, 
btrue: tt
Lemmas referenced : 
false_wf, 
le_wf, 
rel_exp_wf, 
equal_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
cut, 
introduction, 
axiomEquality, 
hypothesis, 
thin, 
rename, 
dependent_pairFormation, 
dependent_set_memberEquality, 
natural_numberEquality, 
independent_pairFormation, 
lambdaFormation, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
applyEquality, 
functionEquality, 
cumulativity, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[x,y:T].    x{}{}R{}\mrightarrow{}y  supposing  x  =  y
Date html generated:
2016_05_13-PM-04_19_20
Last ObjectModification:
2015_12_26-AM-11_33_38
Theory : relations
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