Nuprl Lemma : proof-tree_wf
∀[Sequent,Rule:Type]. ∀[effect:(Sequent × Rule) ⟶ (Sequent List?)]. (proof-tree(Sequent;Rule;effect) ∈ Type)
Proof
Definitions occuring in Statement :
proof-tree: proof-tree(Sequent;Rule;effect),
list: T List,
uall: ∀[x:A]. B[x],
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,
proof-tree: proof-tree(Sequent;Rule;effect),
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
W_wf,
list_wf,
unit_wf2,
int_seg_wf,
length_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
lambdaEquality,
applyEquality,
unionEquality,
hypothesis,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
unionElimination,
natural_numberEquality,
voidEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[Sequent,Rule:Type]. \mforall{}[effect:(Sequent \mtimes{} Rule) {}\mrightarrow{} (Sequent List?)].
(proof-tree(Sequent;Rule;effect) \mmember{} Type)
Date html generated:
2019_10_15-AM-11_06_06
Last ObjectModification:
2018_08_21-PM-01_57_51
Theory : general
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