Nuprl Lemma : mk_applies_split
∀[F,G:Top]. ∀[n,m:ℕ]. (mk_applies(F;G;m + n) ~ mk_applies(mk_applies(F;G;m);λk.(G (m + k));n))
Proof
Definitions occuring in Statement :
mk_applies: mk_applies(F;G;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
add: n + m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
top: Top,
mk_applies: mk_applies(F;G;m),
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
add-commutes,
primrec_add,
top_wf,
int_seg_wf,
nat_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
primrec0_lemma,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
primrec-unroll
Rules used in proof :
sqequalSubstitution,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
because_Cache,
functionExtensionality,
natural_numberEquality,
addEquality,
isect_memberFormation,
sqequalAxiom,
intWeakElimination,
lambdaFormation,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
independent_pairFormation,
computeAll,
independent_functionElimination,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[F,G:Top]. \mforall{}[n,m:\mBbbN{}]. (mk\_applies(F;G;m + n) \msim{} mk\_applies(mk\_applies(F;G;m);\mlambda{}k.(G (m + k));n))
Date html generated:
2017_10_01-AM-08_40_18
Last ObjectModification:
2017_07_26-PM-04_28_00
Theory : untyped!computation
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