Nuprl Lemma : preserved_by_or
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. (R1 preserves P ⇒ R2 preserves P ⇒ R1 ∨ R2 preserves P)
Proof
Definitions occuring in Statement :
rel_or: R1 ∨ R2,
preserved_by: R preserves P,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel_or: R1 ∨ R2,
preserved_by: R preserves P,
infix_ap: x f y,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
or_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
applyEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
Error :inhabitedIsType,
Error :functionIsType,
Error :universeIsType,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[R1,R2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
(R1 preserves P {}\mRightarrow{} R2 preserves P {}\mRightarrow{} R1 \mvee{} R2 preserves P)
Date html generated:
2019_06_20-PM-00_31_11
Last ObjectModification:
2018_09_26-AM-11_56_04
Theory : relations
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