Nuprl - graph_1_1 Citations of not

Def

A == A

False

is mentioned by

Thm* A,B:T List. no_repeats(T;A) (x:T. (x A) (x B)) (x:T. (x A) & (x B)) ||A|| < ||B|| [length_less]

Thm* a,b:T List, t:T. l_disjoint(T;b;[t / a]) (t b) & l_disjoint(T;b;a) [l_disjoint_cons2]

Thm* a,b:T List, t:T. l_disjoint(T;[t / a];b) (t b) & l_disjoint(T;a;b) [l_disjoint_cons]

Thm* R:(AA'Prop), P:(BA), P':(BA'), F,G,H:(BAA), F',G',H':(BA'A'), N:(BA(B List)), N':(BA'(B List)), M:(A), 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)) (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, v:A'. R(u,v) (P(j,u) P'(j,v))) (j:B, u:A, v:A'. R(u,v) P(j,u) P'(j,v) R(F(j,u),F'(j,v))) (j:B, u:A, v:A'. R(u,v) P(j,u) P'(j,v) R(H(j,u),H'(j,v))) (j:B, u:A, v:A'. R(u,v) R(G(j,u),G'(j,v))) (j:B, u:A, v:A'. R(u,v) N(j,u) = N'(j,v)) (j:B, u:A, v:A'. R(u,v) R(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; } ,process v 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-rel]

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]

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]

Thm* (x,y:T. Dec(x = y)) (s:T List, z:T. (z s) (s1,s2:T List. s = (s1 @ [z / s2]) & (z s1))) [l_member_decomp2]

In prior sections: core bool 1 int 2 list 1 sqequal 1 prog 1 rel 1 mb basic mb nat mb list 1 num thy 1 mb list 2

Try larger context: Graphs

graph 1 1 Sections Graphs Doc

`Thm* A,B:T List. no_repeats(T;A) (x:T. (x A) (x B)) (x:T. (x A) & (x B)) \|\|A\|\| < \|\|B\|\|`	[length_less]
`Thm* a,b:T List, t:T. l_disjoint(T;b;[t / a]) (t b) & l_disjoint(T;b;a)`	[l_disjoint_cons2]
`Thm* a,b:T List, t:T. l_disjoint(T;[t / a];b) (t b) & l_disjoint(T;a;b)`	[l_disjoint_cons]
Thm* R:(AA'Prop), P:(BA), P':(BA'), F,G,H:(BAA), F',G',H':(BA'A'), N:(BA(B List)), N':(BA'(B List)), M:(A), 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)) (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, v:A'. R(u,v) (P(j,u) P'(j,v))) (j:B, u:A, v:A'. R(u,v) P(j,u) P'(j,v) R(F(j,u),F'(j,v))) (j:B, u:A, v:A'. R(u,v) P(j,u) P'(j,v) R(H(j,u),H'(j,v))) (j:B, u:A, v:A'. R(u,v) R(G(j,u),G'(j,v))) (j:B, u:A, v:A'. R(u,v) N(j,u) = N'(j,v)) (j:B, u:A, v:A'. R(u,v) R(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; } ,process v 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-rel]
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]
`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]
`Thm* (x,y:T. Dec(x = y)) (s:T List, z:T. (z s) (s1,s2:T List. s = (s1 @ [z / s2]) & (z s1)))`	[l_member_decomp2]