-- file: =and==.mod

in nat+.mod

mod! EQ-NAT{
pr(NAT+)
pred  (_=_) : Nat Nat
var N : Nat
eq (N = N) = true .
}

mod! GOOD-POS{
pr(EQ-NAT)
pred positive : Nat
var N : Nat
eq positive(N) = not (N = 0) .
}

mod! BAD-POS{
pr(NAT+)
pred positive : Nat
var N : Nat
eq positive(N) = not (N == 0) .
}

-- Proof scores for "positive(n) for all Nat n"  (This is not true) .
open BAD-POS
op n : -> Nat .
red positive(n) .
close

-- Proof scores for "positive(n) for all Nat n"  (This is not true) .
open GOOD-POS
op n : -> Nat .
red positive(n) .
close

-- Proof scores for "positive(n) if ((n = 0) = false)  (This is true) .
open GOOD-POS
op n : -> Nat .
eq (n = 0) = false .
red positive(n) .
close