Nuprl Lemma : Memory3-memory-class3
∀[Info,A1,A2,A3,S:Type]. ∀[init:Id ⟶ S]. ∀[tr1:Id ⟶ A1 ⟶ S ⟶ S]. ∀[X1:EClass(A1)]. ∀[tr2:Id ⟶ A2 ⟶ S ⟶ S].
∀[X2:EClass(A2)]. ∀[tr3:Id ⟶ A3 ⟶ S ⟶ S]. ∀[X3:EClass(A3)].
(Memory3(init;tr1;X1;tr2;X2;tr3;X3) = memory-class3(init;tr1;X1;tr2;X2;tr3;X3) ∈ EClass(S))
Proof
Definitions occuring in Statement :
Memory3: Memory3,
memory-class3: memory-class3(init;tr1;X1;tr2;X2;tr3;X3),
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,
Memory3: Memory3,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
State3: State3(init;tr1;X1;tr2;X2;tr3;X3),
squash: ↓T,
prop: ℙ,
true: True,
memory-class3: memory-class3(init;tr1;X1;tr2;X2;tr3;X3),
state-class3: state-class3(init;tr1;X1;tr2;X2;tr3;X3)
Latex:
\mforall{}[Info,A1,A2,A3,S:Type]. \mforall{}[init:Id {}\mrightarrow{} S]. \mforall{}[tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X1:EClass(A1)]. \mforall{}[tr2:Id
{}\mrightarrow{} A2
{}\mrightarrow{} S
{}\mrightarrow{} S].
\mforall{}[X2:EClass(A2)]. \mforall{}[tr3:Id {}\mrightarrow{} A3 {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X3:EClass(A3)].
(Memory3(init;tr1;X1;tr2;X2;tr3;X3) = memory-class3(init;tr1;X1;tr2;X2;tr3;X3))
Date html generated:
2016_05_17-AM-10_06_23
Last ObjectModification:
2016_01_17-PM-11_05_32
Theory : classrel!lemmas
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