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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
prop: ℙ,
guard: {T},
compose: f o g
Latex:
\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:
2016_05_16-AM-10_21_15
Last ObjectModification:
2015_12_28-PM-09_22_39
Theory : new!event-ordering
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