Nuprl Lemma : MMTree-definition
∀[T,A:Type]. ∀[R:A ⟶ MMTree(T) ⟶ ℙ].
  ((∀val:T. {x:A| R[x;MMTree_Leaf(val)]} )
  
⇒ (∀forest:MMTree(T) List List. ((∀u∈forest.(∀u1∈u.{x:A| R[x;u1]} )) 
⇒ {x:A| R[x;MMTree_Node(forest)]} ))
  
⇒ {∀v:MMTree(T). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement : 
MMTree_Node: MMTree_Node(forest)
, 
MMTree_Leaf: MMTree_Leaf(val)
, 
MMTree: MMTree(T)
, 
l_all: (∀x∈L.P[x])
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
guard: {T}
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
set: {x:A| B[x]} 
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s1;s2]
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
prop: ℙ
, 
all: ∀x:A. B[x]
Lemmas referenced : 
MMTree-induction, 
set_wf, 
MMTree_wf, 
all_wf, 
list_wf, 
l_all_wf2, 
l_member_wf, 
MMTree_Node_wf, 
MMTree_Leaf_wf
Rules used in proof : 
cut, 
lemma_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaFormation, 
sqequalRule, 
lambdaEquality, 
applyEquality, 
because_Cache, 
independent_functionElimination, 
cumulativity, 
functionEquality, 
setElimination, 
rename, 
setEquality, 
universeEquality
Latex:
\mforall{}[T,A:Type].  \mforall{}[R:A  {}\mrightarrow{}  MMTree(T)  {}\mrightarrow{}  \mBbbP{}].
    ((\mforall{}val:T.  \{x:A|  R[x;MMTree\_Leaf(val)]\}  )
    {}\mRightarrow{}  (\mforall{}forest:MMTree(T)  List  List
                ((\mforall{}u\mmember{}forest.(\mforall{}u1\mmember{}u.\{x:A|  R[x;u1]\}  ))  {}\mRightarrow{}  \{x:A|  R[x;MMTree\_Node(forest)]\}  ))
    {}\mRightarrow{}  \{\mforall{}v:MMTree(T).  \{x:A|  R[x;v]\}  \})
Date html generated:
2016_05_16-AM-08_55_37
Last ObjectModification:
2015_12_28-PM-06_53_30
Theory : C-semantics
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