Nuprl Lemma : stump-nil
∀T:Type. ∀t:wfd-tree(T). ∀s:ℕ0 ⟶ T. (stump(t) 0 s ~ ¬bempty-wfd-tree(t))
Proof
Definitions occuring in Statement :
stump: stump(t),
empty-wfd-tree: empty-wfd-tree(t),
wfd-tree: wfd-tree(T),
int_seg: {i..j-},
bnot: ¬bb,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
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],
stump: stump(t),
top: Top,
empty-wfd-tree: empty-wfd-tree(t),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
eq_int: (i =z j),
subtract: n - m,
bfalse: ff,
guard: {T},
sq_type: SQType(T)
Lemmas referenced :
subtype_base_sq,
bool_subtype_base,
wfd-tree-induction,
all_wf,
int_seg_wf,
equal_wf,
bool_wf,
false_wf,
le_wf,
bnot_wf,
empty-wfd-tree_wf,
wfd-tree_wf,
wfd_tree_rec_leaf_lemma,
bfalse_wf,
wfd_tree_rec_node_lemma,
btrue_wf,
stump_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
functionEquality,
natural_numberEquality,
cumulativity,
applyEquality,
dependent_set_memberEquality,
independent_pairFormation,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}t:wfd-tree(T). \mforall{}s:\mBbbN{}0 {}\mrightarrow{} T. (stump(t) 0 s \msim{} \mneg{}\msubb{}empty-wfd-tree(t))
Date html generated:
2016_05_14-AM-06_18_19
Last ObjectModification:
2015_12_26-PM-00_03_00
Theory : co-recursion
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