Nuprl Lemma : ispolyform_node_lemma
∀n,b,a:Top. (ispolyform(tree_node(a;b)) n ~ ((ispolyform(a) (n - 1)) ∧b (ispolyform(b) n)) ∧b 0 <z n)
Proof
Definitions occuring in Statement :
ispolyform: ispolyform(p),
tree_node: tree_node(left;right),
band: p ∧b q,
lt_int: i <z j,
top: Top,
all: ∀x:A. B[x],
apply: f a,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
ispolyform: ispolyform(p),
tree_node: tree_node(left;right),
tree_ind: tree_ind,
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}n,b,a:Top.
(ispolyform(tree\_node(a;b)) n \msim{} ((ispolyform(a) (n - 1)) \mwedge{}\msubb{} (ispolyform(b) n)) \mwedge{}\msubb{} 0 <z n)
Date html generated:
2017_10_01-AM-08_32_12
Last ObjectModification:
2017_05_02-PM-00_37_58
Theory : integer!polynomial!trees
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