Nuprl Lemma : cbva_seq_extend
∀[F,G,L:Top]. ∀[m:ℕ].
(cbva_seq(L; λg.let x ⟵ F[g]
in G[g;x]; m) ~ cbva_seq(λn.if (n =z m) then mk_lambdas_fun(λg.F[g];m) else L n fi ;
λg.G[partial_ap(g;m + 1;m);select_fun_ap(g;m + 1;m)]; m + 1))
Proof
Definitions occuring in Statement :
select_fun_ap: select_fun_ap(g;n;m),
partial_ap: partial_ap(g;n;m),
mk_lambdas_fun: mk_lambdas_fun(F;m),
cbva_seq: cbva_seq(L; F; m),
nat: ℕ,
callbyvalueall: callbyvalueall,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
apply: f a,
lambda: λx.A[x],
add: 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: ℕ,
ge: i ≥ j ,
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),
cbva_seq: cbva_seq(L; F; m)
Lemmas referenced :
top_wf,
nat_wf,
primrec0_lemma,
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
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,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_properties,
false_wf,
callbyvalueall_seq-extend
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
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,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[F,G,L:Top]. \mforall{}[m:\mBbbN{}].
(cbva\_seq(L; \mlambda{}g.let x \mleftarrow{}{} F[g]
in G[g;x]; m)
\msim{} cbva\_seq(\mlambda{}n.if (n =\msubz{} m) then mk\_lambdas\_fun(\mlambda{}g.F[g];m) else L n fi ;
\mlambda{}g.G[partial\_ap(g;m + 1;m);select\_fun\_ap(g;m + 1;m)]; m + 1))
Date html generated:
2016_05_15-PM-02_14_51
Last ObjectModification:
2016_01_15-PM-10_17_49
Theory : untyped!computation
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