Nuprl Lemma : mk_applies_lambdas_fun1
∀[F,G:Top]. ∀[m:ℕ]. ∀[n:ℕm + 1].
(mk_applies(mk_lambdas_fun(F;n);G;m) ~ mk_applies(F (λx.mk_applies(x;G;n));λi.(G (n + i));m - n))
Proof
Definitions occuring in Statement :
mk_applies: mk_applies(F;G;m),
mk_lambdas_fun: mk_lambdas_fun(F;m),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
subtract: n - m,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
exists: ∃x:A. B[x],
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),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
top_wf,
nat_wf,
int_seg_wf,
mk_applies_lambdas_fun0,
mk_applies_split,
int_subtype_base,
subtype_base_sq,
equal_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
le_wf,
int_formula_prop_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermAdd_wf,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
subtract_wf,
int_seg_properties
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
natural_numberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
dependent_pairFormation,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
because_Cache,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[F,G:Top]. \mforall{}[m:\mBbbN{}]. \mforall{}[n:\mBbbN{}m + 1].
(mk\_applies(mk\_lambdas\_fun(F;n);G;m) \msim{} mk\_applies(F (\mlambda{}x.mk\_applies(x;G;n));\mlambda{}i.(G (n + i));m - n))
Date html generated:
2016_05_15-PM-02_11_46
Last ObjectModification:
2016_01_15-PM-10_20_04
Theory : untyped!computation
Home
Index