Nuprl - graph_1_1 LEMMAs for accumulate_DASH

Rank	Theorem	Name
3	Thm* M:(A), Q:(BAAProp), P:(BA), F,G,H:(BAA), N:(BA(B List)). (i:B, s:A. P(i,s) M(F(i,s))M(s)) (i:B, s:A. M(G(i,s))M(s)) (i:B, s:A. P(i,s) M(H(i,s)) < M(s)) (j:B, u:A. P(j,u) Q(j,u,F(j,u))) (j:B, u,z:A. P(j,u) Q(j,H(j,u),z) Q(j,u,G(j,z))) (j:B, u:A. Q(j,u,u)) (i,j:B, u,v,z:A. Q(i,u,v) Q(j,v,z) Q(j,u,z)) (j:B, u:A. Q(j,u,process u j where process s i == if P(i,s) then F(i,s) else G(i,s) where xs := N(i,s); s:= H(i,s); while not null xs { s := process s (hd xs); xs := tl xs; } ))	[accumulate-induction1]
cites
0	Thm* A,B:Type, P:(BA), F,G,H:(BAA), N:(BA(B List)), M:(A). (i:B, s:A. P(i,s) M(F(i,s))M(s)) (i:B, s:A. M(G(i,s))M(s)) (i:B, s:A. P(i,s) M(H(i,s)) < M(s)) (j:B, u:A. process u j where process s i == if P(i,s) then F(i,s) else G(i,s) where xs := N(i,s); s:= H(i,s); while not null xs { s := process s (hd xs); xs := tl xs; } {s:A\| M(s)M(u) })	[accumulate_wf]
2	Thm* L1,L2,L3:T List. L1 L2 L2 L3 L1 L3	[sublist_transitivity]
1	Thm* L1,L2:T List. L1 = L2 L1 L2	[sublist_weakening]
2	Thm* L1,L2:T List. null(L2) L1 tl(L2) L1 L2	[sublist_tl]