Nuprl Lemma : simple-cbva-seq-spread
∀[F,G,H,L:Top]. ∀[m:ℕ+].
(let x,y = simple-cbva-seq(L;λa.<F[a], G[a]>;m)
in H[x;y] ~ simple-cbva-seq(L;λa.H[F[a];G[a]];m))
Proof
Definitions occuring in Statement :
simple-cbva-seq: simple-cbva-seq(L;F;m),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
lambda: λx.A[x],
spread: spread def,
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
simple-cbva-seq: simple-cbva-seq(L;F;m),
cbva-seq: cbva-seq(L;F;m),
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
nat_plus_properties,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
callbyvalueall-seq-spread0,
less_than_wf,
nat_plus_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
dependent_set_memberEquality,
sqequalAxiom
Latex:
\mforall{}[F,G,H,L:Top]. \mforall{}[m:\mBbbN{}\msupplus{}].
(let x,y = simple-cbva-seq(L;\mlambda{}a.<F[a], G[a]>m)
in H[x;y] \msim{} simple-cbva-seq(L;\mlambda{}a.H[F[a];G[a]];m))
Date html generated:
2017_10_01-AM-08_41_22
Last ObjectModification:
2017_07_26-PM-04_28_36
Theory : untyped!computation
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