Nuprl Lemma : State1-state-class1
∀[Info,B,A:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[init:Id ⟶ B]. ∀[X:EClass(A)].
(State1(init;f;X) = state-class1(init;f;X) ∈ EClass(B))
Proof
Definitions occuring in Statement :
State1: State1(init;tr;X),
state-class1: state-class1(init;tr;X),
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
state-class1: state-class1(init;tr;X),
State1: State1(init;tr;X),
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[X:EClass(A)].
(State1(init;f;X) = state-class1(init;f;X))
Date html generated:
2016_05_17-AM-10_04_33
Last ObjectModification:
2015_12_29-PM-03_52_26
Theory : classrel!lemmas
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