Nuprl Lemma : tree-height_wf
∀[x:Type]. ∀[t:tree(x)]. (tree-height(t) ∈ ℕ)
Proof
Definitions occuring in Statement :
tree-height: tree-height(t),
tree: tree(E),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tree-height: tree-height(t),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
all: ∀x:A. B[x],
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
tree_ind_wf_simple,
top_wf,
nat_wf,
tree_subtype,
false_wf,
le_wf,
imax_wf,
imax_nat,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_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_eq_lemma,
int_formula_prop_wf,
equal_wf,
tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll,
independent_functionElimination,
axiomEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[x:Type]. \mforall{}[t:tree(x)]. (tree-height(t) \mmember{} \mBbbN{})
Date html generated:
2017_10_01-AM-08_30_42
Last ObjectModification:
2017_05_02-AM-10_59_05
Theory : tree_1
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