Nuprl Lemma : proveable_wf
∀[Sequent,Rule:Type]. ∀[effect:(Sequent × Rule) ⟶ (Sequent List?)]. ∀[s:Sequent].
(proveable(Sequent;Rule;effect;s) ∈ ℙ)
Proof
Definitions occuring in Statement :
proveable: proveable(Sequent;Rule;effect;s),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
proveable: proveable(Sequent;Rule;effect;s),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
sq_exists_wf,
proof-tree_wf,
correct_proof_wf,
list_wf,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
productEquality,
unionEquality,
universeEquality
Latex:
\mforall{}[Sequent,Rule:Type]. \mforall{}[effect:(Sequent \mtimes{} Rule) {}\mrightarrow{} (Sequent List?)]. \mforall{}[s:Sequent].
(proveable(Sequent;Rule;effect;s) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_15_17
Last ObjectModification:
2015_12_27-PM-01_02_30
Theory : general
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