Step
*
of Lemma
fpf-sub_functionality2
∀[A,A':Type].
∀[B:A ⟶ Type]. ∀[C:A' ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[eq':EqDecider(A')]. ∀[f,g:a:A fp-> B[a]].
{f ⊆ g supposing f ⊆ g} supposing ∀a:A. (B[a] ⊆r C[a])
supposing strong-subtype(A;A')
BY
{ xxx((InstLemma `fpf-sub-functionality2` []) THEN Unfold `guard` 0 THEN Trivial)xxx }
Latex:
Latex:
\mforall{}[A,A':Type].
\mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[C:A' {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[eq':EqDecider(A')]. \mforall{}[f,g:a:A fp-> B[a]].
\{f \msubseteq{} g supposing f \msubseteq{} g\} supposing \mforall{}a:A. (B[a] \msubseteq{}r C[a])
supposing strong-subtype(A;A')
By
Latex:
xxx((InstLemma `fpf-sub-functionality2` []) THEN Unfold `guard` 0 THEN Trivial)xxx
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