Nuprl Lemma : TC_wf
∀[Dom:Type]. ∀[F:Dom ⟶ Dom ⟶ ℙ]. ∀[a,b:Dom]. (TC(λx,y.F[x;y])(a,b) ∈ ℙ)
Proof
Definitions occuring in Statement :
TC: TC(λx,y.F[x; y])(a,b),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
TC: TC(λx,y.F[x; y])(a,b),
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
transitive-closure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[Dom:Type]. \mforall{}[F:Dom {}\mrightarrow{} Dom {}\mrightarrow{} \mBbbP{}]. \mforall{}[a,b:Dom]. (TC(\mlambda{}x,y.F[x;y])(a,b) \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-09_07_39
Last ObjectModification:
2015_12_28-PM-07_02_59
Theory : first-order!and!ancestral!logic
Home
Index