Nuprl Lemma : rel_rev_implies_weakening
∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ].  (R1 
⇐⇒ R2 
⇒ R1 
⇐ R2)
Proof
Definitions occuring in Statement : 
rel_rev_implies: R1 
⇐ R2
, 
rel_equivalent: R1 
⇐⇒ R2
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
rel_rev_implies: R1 
⇐ R2
, 
rel_equivalent: R1 
⇐⇒ R2
, 
rel_implies: R1 => R2
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
infix_ap: x f y
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
all_wf, 
iff_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
lambdaFormation, 
cut, 
hypothesis, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
productElimination, 
independent_functionElimination, 
applyEquality, 
lemma_by_obid, 
isectElimination, 
lambdaEquality, 
functionEquality, 
cumulativity, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[R1,R2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (R1  \mLeftarrow{}{}\mRightarrow{}  R2  {}\mRightarrow{}  R1  \mLeftarrow{}{}  R2)
Date html generated:
2016_05_14-AM-06_04_48
Last ObjectModification:
2015_12_26-AM-11_33_03
Theory : relations
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