Nuprl Lemma : mk_applies_lambdas1
∀[F,G:Top]. ∀[n:ℕ]. ∀[m:ℕn + 1]. (mk_applies(mk_lambdas(F;m);G;n) ~ mk_applies(F;λk.(G (m + k));n - m))
Proof
Definitions occuring in Statement :
mk_applies: mk_applies(F;G;m),
mk_lambdas: mk_lambdas(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 :
exists: ∃x:A. B[x],
member: t ∈ T,
nat: ℕ,
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
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),
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
top_wf,
nat_wf,
int_seg_wf,
mk_applies_lambdas2,
false_wf,
int_seg_subtype_nat,
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,
int_seg_properties,
subtract_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairFormation,
dependent_set_memberEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
addEquality,
productElimination,
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,
applyEquality,
lambdaFormation,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[F,G:Top]. \mforall{}[n:\mBbbN{}]. \mforall{}[m:\mBbbN{}n + 1].
(mk\_applies(mk\_lambdas(F;m);G;n) \msim{} mk\_applies(F;\mlambda{}k.(G (m + k));n - m))
Date html generated:
2016_05_15-PM-02_10_36
Last ObjectModification:
2016_01_15-PM-10_20_47
Theory : untyped!computation
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