Step
*
of Lemma
uand-subtype1
∀[A,B:Type]. ∀[z:uand(A;B)]. (z ∈ A)
BY
{ TACTIC:(Auto THEN (With ⌜Ax⌝ (D (-1))⋅ THENA Auto) THEN Reduce (-1)) }
1
1. A : Type
2. B : Type
3. z : ⋂x:Base. ⋂p:(x)↓. if x = Ax then A otherwise B
4. y : ⋂p:(Ax)↓. if Ax = Ax then A otherwise B
5. y = z ∈ (⋂p:0 ≤ 0. A)
⊢ z ∈ A
Latex:
Latex:
\mforall{}[A,B:Type]. \mforall{}[z:uand(A;B)]. (z \mmember{} A)
By
Latex:
TACTIC:(Auto THEN (With \mkleeneopen{}Ax\mkleeneclose{} (D (-1))\mcdot{} THENA Auto) THEN Reduce (-1))
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