Nuprl Lemma : proof-abort_wf
∀[Sequent,Rule:Type]. ∀[effect:(Sequent × Rule) ⟶ (Sequent List?)]. ∀[s:Sequent]. ∀[r:Rule].
proof-abort(s;r) ∈ proof-tree(Sequent;Rule;effect) supposing ↑isr(effect <s, r>)
Proof
Definitions occuring in Statement :
proof-abort: proof-abort(s;r),
proof-tree: proof-tree(Sequent;Rule;effect),
list: T List,
assert: ↑b,
isr: isr(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
pair: <a, b>,
product: x:A × B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
proof-abort: proof-abort(s;r),
all: ∀x:A. B[x],
implies: P ⇒ Q,
isr: isr(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
btrue: tt,
ext-eq: A ≡ B,
and: P ∧ Q
Lemmas referenced :
assert_wf,
isr_wf,
list_wf,
unit_wf2,
int_seg_wf,
length_wf,
equal_wf,
proof-tree_wf,
false_wf,
true_wf,
proof-tree-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
independent_pairEquality,
isect_memberEquality,
because_Cache,
functionEquality,
productEquality,
unionEquality,
universeEquality,
dependent_pairEquality,
lambdaFormation,
unionElimination,
natural_numberEquality,
voidEquality,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
functionExtensionality,
productElimination
Latex:
\mforall{}[Sequent,Rule:Type]. \mforall{}[effect:(Sequent \mtimes{} Rule) {}\mrightarrow{} (Sequent List?)]. \mforall{}[s:Sequent]. \mforall{}[r:Rule].
proof-abort(s;r) \mmember{} proof-tree(Sequent;Rule;effect) supposing \muparrow{}isr(effect <s, r>)
Date html generated:
2019_10_15-AM-11_06_19
Last ObjectModification:
2018_08_21-PM-01_58_14
Theory : general
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