Nuprl Lemma : unroll-prec-size
∀[a,i,x:Top]. (||i;x|| ~ let lbl,z = x in 1 + add-sz(pcorec-size(lbl,p.a[lbl;p]);a[lbl;i];z))
Proof
Definitions occuring in Statement :
prec-size: ||i;x||,
pcorec-size: pcorec-size(lbl,p.a[lbl; p]),
add-sz: add-sz(sz;L;x),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
spread: spread def,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
prec-size: ||i;x||,
so_lambda: λ2x y.t[x; y],
member: t ∈ T,
top: Top,
so_apply: x[s1;s2]
Lemmas referenced :
unroll-pcorec-size,
istype-void,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :isect_memberEquality_alt,
voidElimination,
hypothesis,
because_Cache,
Error :inhabitedIsType,
hypothesisEquality
Latex:
\mforall{}[a,i,x:Top]. (||i;x|| \msim{} let lbl,z = x in 1 + add-sz(pcorec-size(lbl,p.a[lbl;p]);a[lbl;i];z))
Date html generated:
2019_06_20-PM-02_05_04
Last ObjectModification:
2019_02_22-PM-06_15_20
Theory : tuples
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