Nuprl Lemma : mk_lambdas_compose
∀[F:Top]. ∀[n,m:ℕ]. (mk_lambdas(mk_lambdas(F;n);m) ~ mk_lambdas(F;n + m))
Proof
Definitions occuring in Statement :
mk_lambdas: mk_lambdas(F;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
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],
top: Top,
and: P ∧ Q,
prop: ℙ,
mk_lambdas: mk_lambdas(F;m),
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
top_wf,
nat_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
int_subtype_base,
subtype_base_sq,
int_term_value_add_lemma,
itermAdd_wf,
decidable__lt,
mk_lambdas_unroll,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
add-zero,
primrec0_lemma,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
because_Cache,
unionElimination,
dependent_set_memberEquality,
addEquality,
instantiate,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[F:Top]. \mforall{}[n,m:\mBbbN{}]. (mk\_lambdas(mk\_lambdas(F;n);m) \msim{} mk\_lambdas(F;n + m))
Date html generated:
2016_05_15-PM-02_10_05
Last ObjectModification:
2016_01_15-PM-10_21_04
Theory : untyped!computation
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