CADiZ

Reference manual / Z-related commands / Proof rule commands / total functionality


The total functionality command is applicable to a name in a goal, where the name refers to an injection of a free type. It makes the total functionality 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 total functionality constraint for an injection is

\forall x : ei,k @ \exists1 y : gi,k @ y . 1 = x

Tactic example

"total functionality" e1 e2

This example applies the total functionality command to expressions e1 and e2.


IT 19-Feb-1999