Nuprl Lemma : make-proof-tree_wf
∀[Sequent,Rule:Type]. ∀[effect:(Sequent × Rule) ⟶ (Sequent List?)]. ∀[s:Sequent]. ∀[r:Rule].
∀[L:proof-tree(Sequent;Rule;effect) List].
(make-proof-tree(s;r;L) ∈ proof-tree(Sequent;Rule;effect)) supposing
((||L|| = ||outl(effect <s, r>)|| ∈ ℤ) and
(↑isl(effect <s, r>)))
Proof
Definitions occuring in Statement :
make-proof-tree: make-proof-tree(s;r;L),
proof-tree: proof-tree(Sequent;Rule;effect),
length: ||as||,
list: T List,
outl: outl(x),
assert: ↑b,
isl: isl(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,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
outl: outl(x),
isl: isl(x),
and: P ∧ Q,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
make-proof-tree: make-proof-tree(s;r;L),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
bfalse: ff,
ext-eq: A ≡ B
Lemmas referenced :
equal_wf,
length_wf,
proof-tree_wf,
list_wf,
unit_wf2,
assert_elim,
isl_wf,
bfalse_wf,
and_wf,
btrue_neq_bfalse,
assert_wf,
int_seg_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
intformeq_wf,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma,
true_wf,
false_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,
intEquality,
hypothesisEquality,
applyEquality,
independent_pairEquality,
unionEquality,
lambdaFormation,
unionElimination,
independent_isectElimination,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename,
productElimination,
independent_functionElimination,
voidElimination,
dependent_functionElimination,
isect_memberEquality,
because_Cache,
functionEquality,
productEquality,
universeEquality,
dependent_pairEquality,
natural_numberEquality,
voidEquality,
lambdaEquality,
cumulativity,
functionExtensionality,
approximateComputation,
dependent_pairFormation,
int_eqEquality
Latex:
\mforall{}[Sequent,Rule:Type]. \mforall{}[effect:(Sequent \mtimes{} Rule) {}\mrightarrow{} (Sequent List?)]. \mforall{}[s:Sequent]. \mforall{}[r:Rule].
\mforall{}[L:proof-tree(Sequent;Rule;effect) List].
(make-proof-tree(s;r;L) \mmember{} proof-tree(Sequent;Rule;effect)) supposing
((||L|| = ||outl(effect <s, r>)||) and
(\muparrow{}isl(effect <s, r>)))
Date html generated:
2019_10_15-AM-11_06_14
Last ObjectModification:
2018_08_21-PM-01_58_00
Theory : general
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