Nuprl Lemma : wfd_tree_rec_node_lemma
∀F,f,F,b:Top. (wfd-tree-rec(b;r.F[r];Wsup(ff;f)) ~ F[λx.wfd-tree-rec(b;r.F[r];f x)])
Proof
Definitions occuring in Statement :
wfd-tree-rec: wfd-tree-rec(b;r.F[r];t),
Wsup: Wsup(a;b),
bfalse: ff,
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
wfd-tree-rec: wfd-tree-rec(b;r.F[r];t),
W-rec: W-rec(a,f,r.F[a; f; r];w),
Wsup: Wsup(a;b),
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule
Latex:
\mforall{}F,f,F,b:Top. (wfd-tree-rec(b;r.F[r];Wsup(ff;f)) \msim{} F[\mlambda{}x.wfd-tree-rec(b;r.F[r];f x)])
Date html generated:
2016_05_14-AM-06_17_58
Last ObjectModification:
2015_12_26-PM-00_03_17
Theory : co-recursion
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