### 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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