Nuprl Lemma : b-union-base-equality
∀A:Type. ∀a,b:Base. ((a = b ∈ (Base ⋃ A)) ⇒ (b ∈ A) ⇒ (a = b ∈ A))
Proof
Definitions occuring in Statement :
b-union: A ⋃ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
base: Base,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
strong-subtype-union-base,
strong-subtype-implies,
b-union_wf,
base_wf,
istype-universe,
istype-base
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
instantiate,
universeEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
Error :equalityIstype,
Error :universeIsType,
sqequalBase,
because_Cache
Latex:
\mforall{}A:Type. \mforall{}a,b:Base. ((a = b) {}\mRightarrow{} (b \mmember{} A) {}\mRightarrow{} (a = b))
Date html generated:
2019_06_20-PM-00_28_06
Last ObjectModification:
2018_12_07-AM-11_43_12
Theory : subtype_1
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