Nuprl Lemma : rel_exp0
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀x,y:T. (x R^0 y ⇐⇒ x = y ∈ T)
Proof
Definitions occuring in Statement :
rel_exp: R^n,
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
infix_ap: x f y,
rel_exp: R^n,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
btrue: tt,
member: t ∈ T,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
rev_implies: P ⇐ Q
Lemmas referenced :
infix_ap_wf,
rel_exp_wf,
false_wf,
le_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
sqequalHypSubstitution,
hypothesis,
thin,
instantiate,
lemma_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
universeEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}x,y:T. (x rel\_exp(T; R; 0) y \mLeftarrow{}{}\mRightarrow{} x = y)
Date html generated:
2016_05_14-PM-03_52_04
Last ObjectModification:
2015_12_26-PM-06_57_20
Theory : relations2
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