CADiZ

Reference manual / Z-related commands / Proof rule commands / membership


The membership command is applicable to a name in a goal, where the name refers to an element or injection of a free type. It makes the membership constraint implied by the free type available as an antecedent in the sub-goal.

Given the general form of a free type,

f1 ::= h1,1 ... h1,m1 | g1,1 \ldata e1,1 \rdata ... g1,n \ldata e1,n \rdata
& ... &
fr ::= hr,1 ... hr,mr | gr,1 \ldata er,1 \rdata ... gr,nr \ldata er,nr \rdata

the membership constraint for an element is

hi,j \in fi

and the membership constraint for an injection is

gi,k \in \power (ei,k \cross fi)

Tactic example

"membership" e1 e2

This example applies the membership command to expressions e1 and e2.


IT 19-Feb-1999