Nuprl Lemma : mk_lambdas_fun_lambdas1
∀[f:Top]. ∀[k,m:ℕ]. ∀[n:ℕm + 1].
(mk_lambdas_fun(λh.mk_lambdas(h mk_lambdas(f;n);k);m) ~ mk_lambdas(mk_lambdas_fun(λg.mk_lambdas(g f;k);m - n);n))
Proof
Definitions occuring in Statement :
mk_lambdas: mk_lambdas(F;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,
all: ∀x:A. B[x],
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,
top: Top,
and: P ∧ Q,
prop: ℙ,
mk_lambdas: mk_lambdas(F;m),
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
nat_plus: ℕ+,
le: A ≤ B,
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
int_seg: {i..j-},
lelt: i ≤ j < k
Lemmas referenced :
top_wf,
int_seg_wf,
int_term_value_add_lemma,
itermAdd_wf,
int_seg_properties,
false_wf,
int_seg_subtype_nat,
nat_wf,
mk_lambdas_unroll,
less_than_transitivity1,
mk_lambdas_fun-unroll-first,
primrec1_lemma,
decidable__le,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
subtract_wf,
decidable__equal_int,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
primrec0_lemma,
le_wf,
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,
sqequalRule,
thin,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
because_Cache,
instantiate,
unionElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
productElimination,
applyEquality,
addEquality
Latex:
\mforall{}[f:Top]. \mforall{}[k,m:\mBbbN{}]. \mforall{}[n:\mBbbN{}m + 1].
(mk\_lambdas\_fun(\mlambda{}h.mk\_lambdas(h mk\_lambdas(f;n);k);m)
\msim{} mk\_lambdas(mk\_lambdas\_fun(\mlambda{}g.mk\_lambdas(g f;k);m - n);n))
Date html generated:
2016_05_15-PM-02_11_22
Last ObjectModification:
2016_01_15-PM-10_20_22
Theory : untyped!computation
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