Nuprl Lemma : mk_applies_unroll
∀[F,G:Top]. ∀[m:ℕ+]. (mk_applies(F;G;m) ~ mk_applies(F;G;m - 1) (G (m - 1)))
Proof
Definitions occuring in Statement :
mk_applies: mk_applies(F;G;m),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk_applies: mk_applies(F;G;m),
nat_plus: ℕ+,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
primrec-unroll,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_plus_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nat_plus_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
independent_pairFormation,
computeAll,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[F,G:Top]. \mforall{}[m:\mBbbN{}\msupplus{}]. (mk\_applies(F;G;m) \msim{} mk\_applies(F;G;m - 1) (G (m - 1)))
Date html generated:
2017_10_01-AM-08_40_20
Last ObjectModification:
2017_07_26-PM-04_28_02
Theory : untyped!computation
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