Step
*
of Lemma
fun-sep-co-trans
∀[A:Type]. ∀ss:SeparationSpace. ∀f,g,h:A ⟶ Point. (fun-sep(ss;A;f;g)
⇒ (fun-sep(ss;A;f;h) ∨ fun-sep(ss;A;g;h)))
BY
{ (Auto
THEN D -1
THEN (InstLemma `ss-sep-or` [⌜ss⌝;⌜f a⌝;⌜g a⌝;⌜h a⌝]⋅ THENA Auto)
THEN ParallelLast
THEN D 0 With ⌜a⌝
THEN Auto) }
Latex:
Latex:
\mforall{}[A:Type]
\mforall{}ss:SeparationSpace. \mforall{}f,g,h:A {}\mrightarrow{} Point.
(fun-sep(ss;A;f;g) {}\mRightarrow{} (fun-sep(ss;A;f;h) \mvee{} fun-sep(ss;A;g;h)))
By
Latex:
(Auto
THEN D -1
THEN (InstLemma `ss-sep-or` [\mkleeneopen{}ss\mkleeneclose{};\mkleeneopen{}f a\mkleeneclose{};\mkleeneopen{}g a\mkleeneclose{};\mkleeneopen{}h a\mkleeneclose{}]\mcdot{} THENA Auto)
THEN ParallelLast
THEN D 0 With \mkleeneopen{}a\mkleeneclose{}
THEN Auto)
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