Nuprl Lemma : preserved_by_wf
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀[R:T ⟶ T ⟶ ℙ]. (R preserves P ∈ ℙ)
Proof
Definitions occuring in Statement :
preserved_by: R preserves P,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
preserved_by: R preserves P,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
infix_ap: x f y,
so_apply: x[s]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
Error :inhabitedIsType,
isect_memberEquality,
cumulativity,
universeEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (R preserves P \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_30_28
Last ObjectModification:
2018_09_26-PM-00_39_27
Theory : relations
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