u perspek - Filozofski fakultet u Splitu

k∀x (P (x) → Q(x))k = k∃xP (x) → Q(x)k
| {z } | {z }
a
b
k∀x (P (x) → Q(x))k =
| {z }
a
⎧ ¯
⎫
⎨ ¯ h = µ g∧
⎬
= hg, hi ¯
⎩ ¯ k [x] h →
¯ ∀k
⎭
∃m : hk, mi ∈kP (x) → Q(x)k
⎧ ¯
⎫
¯ h = ⎛g∧
⎞
⎪⎨ ¯ k [x] h →
⎪⎬
¯
= hg, hi ¯ ⎜ ¯
¯ ∀k ⎜ ¯ m = k
⎟
¯
⎟
⎝
⎪⎩ ¯ ∃m ¯ ¯
¯
¯ ¯ ∧∀i ¯ hm, ii ∈kP (x)k → ⎠
⎪⎭
¯ ∃j : hi, ji ∈kQ(x)k
⎧ ¯
⎫
¯
⎪⎨ ¯ h = ⎛g∧
⎞ ⎪⎬
¯
= hg, hi ¯ k [x] µ h →
¯
⎪⎩ ¯ ∀k ⎝ hk, ii ∈kP (x)k → ⎠
¯ ∀i
⎪⎭
∃j : hi, ji ∈kQ(x)k
⎧ ¯
⎫
¯
⎪⎨ ¯ h = ⎛g∧
⎞ ⎪⎬
¯
= hg, hi ¯ k [x] µ h →
¯
⎪⎩ ¯ ∀k ⎝ (k = i ∧ i(x) ∈ I(P )) → ⎠
¯ ∀i
⎪⎭
∃j (i = j ∧ j(x) ∈ I(Q))
= {hg, gi |∀k(k [x] g → (k(x) ∈ I(P )) → k(x) ∈ I(Q)))}
= {hg, gi |∀k ((k [x] g ∧ k(x) ∈ I(P )) → k(x) ∈ I(Q))}
| {z }
a
163