Nuprl Lemma : callbyvalueall-seq-spread0
∀[F,G,H,L:Top]. ∀[m:ℕ+].
(let x,y = callbyvalueall-seq(L;λx.x;mk_lambdas(λa.<F[a], G[a]>;m - 1);0;m)
in H[x;y] ~ callbyvalueall-seq(L;λx.x;mk_lambdas(λa.H[F[a];G[a]];m - 1);0;m))
Proof
Definitions occuring in Statement :
mk_lambdas: mk_lambdas(F;m),
callbyvalueall-seq: callbyvalueall-seq(L;G;F;n;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>,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
mk_applies: mk_applies(F;G;m)
Lemmas referenced :
top_wf,
nat_plus_wf,
primrec0_lemma,
lelt_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_plus_properties,
false_wf,
callbyvalueall-seq-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
lambdaFormation,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
addEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[F,G,H,L:Top]. \mforall{}[m:\mBbbN{}\msupplus{}].
(let x,y = callbyvalueall-seq(L;\mlambda{}x.x;mk\_lambdas(\mlambda{}a.<F[a], G[a]>m - 1);0;m)
in H[x;y] \msim{} callbyvalueall-seq(L;\mlambda{}x.x;mk\_lambdas(\mlambda{}a.H[F[a];G[a]];m - 1);0;m))
Date html generated:
2016_05_15-PM-02_12_33
Last ObjectModification:
2016_01_15-PM-10_19_59
Theory : untyped!computation
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