Nuprl Lemma : change-equality-type
∀[A,B:Type]. (respects-equality(A;B) ⇒ (∀x,y:A. ((x = y ∈ A) ⇒ (x ∈ B) ⇒ (x = y ∈ B))))
Proof
Definitions occuring in Statement :
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
respects-equality: respects-equality(S;T)
Lemmas referenced :
respects-equality_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
sqequalRule,
Error :equalityIstype,
Error :universeIsType,
hypothesisEquality,
cut,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
independent_functionElimination,
because_Cache,
introduction,
extract_by_obid,
isectElimination,
Error :inhabitedIsType,
universeEquality,
pointwiseFunctionalityForEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A,B:Type]. (respects-equality(A;B) {}\mRightarrow{} (\mforall{}x,y:A. ((x = y) {}\mRightarrow{} (x \mmember{} B) {}\mRightarrow{} (x = y))))
Date html generated:
2019_06_20-AM-11_13_51
Last ObjectModification:
2018_11_28-PM-11_36_14
Theory : core_2
Home
Index