Step
*
of Lemma
fpf-cap_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:a:A fp-> B[a]]. ∀[eq:EqDecider(A)]. ∀[x:A]. ∀[z:B[x]]. (f(x)?z ∈ B[x])
BY
{ xxx(Auto THEN Unfold `fpf-cap` 0 THEN SplitOnConclITE THEN Auto THEN FpfSubtype)xxx }
Latex:
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x:A]. \mforall{}[z:B[x]].
(f(x)?z \mmember{} B[x])
By
Latex:
xxx(Auto THEN Unfold `fpf-cap` 0 THEN SplitOnConclITE THEN Auto THEN FpfSubtype)xxx
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