Nuprl Lemma : transitive-closure_wf
∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ]. (TC(R) ∈ A ⟶ A ⟶ ℙ)
Proof
Definitions occuring in Statement :
transitive-closure: TC(R),
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,
transitive-closure: TC(R),
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
set_wf,
list_wf,
and_wf,
rel_path_wf,
less_than_wf,
length_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
applyEquality,
hypothesis,
universeEquality,
natural_numberEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (TC(R) \mmember{} A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_51_07
Last ObjectModification:
2015_12_26-PM-06_58_33
Theory : relations2
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