Nuprl Lemma : inject-composes
∀[A,B0,B1,C:Type]. ∀[f:A ─→ B0]. ∀[g:B1 ─→ C].
(Inj(A;C;g o f)) supposing (Inj(B1;C;g) and Inj(A;B0;f) and strong-subtype(B0;B1))
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
inject: Inj(A;B;f),
compose: f o g,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
strong-subtype-implies,
equal_wf
\mforall{}[A,B0,B1,C:Type]. \mforall{}[f:A {}\mrightarrow{} B0]. \mforall{}[g:B1 {}\mrightarrow{} C].
(Inj(A;C;g o f)) supposing (Inj(B1;C;g) and Inj(A;B0;f) and strong-subtype(B0;B1))
Date html generated:
2015_07_17-AM-09_04_01
Last ObjectModification:
2015_01_27-PM-00_53_44
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