Nuprl Lemma : disjoint-union-tr_wf
∀[A,B,S:Type]. ∀[tr1:Id ─→ A ─→ S ─→ S]. ∀[tr2:Id ─→ B ─→ S ─→ S]. (tr1 + tr2 ∈ Id ─→ (A + B) ─→ S ─→ S)
Proof
Definitions occuring in Statement :
disjoint-union-tr: tr1 + tr2,
Id: Id,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
union: left + right,
universe: Type
Lemmas :
isl_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
not_assert_elim,
btrue_wf,
btrue_neq_bfalse,
Id_wf
Latex:
\mforall{}[A,B,S:Type]. \mforall{}[tr1:Id {}\mrightarrow{} A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[tr2:Id {}\mrightarrow{} B {}\mrightarrow{} S {}\mrightarrow{} S].
(tr1 + tr2 \mmember{} Id {}\mrightarrow{} (A + B) {}\mrightarrow{} S {}\mrightarrow{} S)
Date html generated:
2015_07_22-PM-00_07_21
Last ObjectModification:
2015_01_28-AM-11_42_24
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