Nuprl Lemma : equal-wf
∀[X,Y,A:Type]. (respects-equality(Y;A) ⇒ respects-equality(X;A) ⇒ (∀[a:X]. ∀[b:Y]. (a = b ∈ A ∈ ℙ)))
Proof
Definitions occuring in Statement :
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
member: t ∈ T,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
member: t ∈ T,
label: ...$L... t,
guard: {T},
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x]
Lemmas referenced :
respects-equality_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :universeIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
Error :inhabitedIsType,
universeEquality,
equalityEquality,
dependent_functionElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X,Y,A:Type]. (respects-equality(Y;A) {}\mRightarrow{} respects-equality(X;A) {}\mRightarrow{} (\mforall{}[a:X]. \mforall{}[b:Y]. (a = b \mmember{} \mBbbP{})))
Date html generated:
2019_06_20-AM-11_13_47
Last ObjectModification:
2018_11_25-PM-06_16_49
Theory : core_2
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