Nuprl Lemma : partial_ap_of_partial_ap_gen
∀[g:Top]. ∀[m1:ℕ]. ∀[m2:ℕm1 + 1]. ∀[m3:ℕ(m1 - m2) + 1]. ∀[m4:ℕm3 + 1].
(partial_ap(partial_ap_gen(g;m1;m2;m3);m3;m4) ~ partial_ap_gen(g;m1;m2;m4))
Proof
Definitions occuring in Statement :
partial_ap: partial_ap(g;n;m),
partial_ap_gen: partial_ap_gen(g;n;s;m),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
subtract: n - m,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
partial_ap_gen: partial_ap_gen(g;n;s;m),
partial_ap: partial_ap(g;n;m),
top: Top,
nat: ℕ,
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),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
sq_type: SQType(T),
mk_lambdas_fun: mk_lambdas_fun(F;m),
mk_lambdas-fun: mk_lambdas-fun(F;G;n;m),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
top_wf,
nat_wf,
int_seg_wf,
mk_lambdas_compose,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
int_subtype_base,
subtype_base_sq,
lelt_wf,
decidable__lt,
mk_lambdas_fun_lambdas1,
false_wf,
int_seg_subtype_nat,
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,
mk_lambdas_fun_compose1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
productElimination,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
applyEquality,
addEquality,
lambdaFormation,
instantiate,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[g:Top]. \mforall{}[m1:\mBbbN{}]. \mforall{}[m2:\mBbbN{}m1 + 1]. \mforall{}[m3:\mBbbN{}(m1 - m2) + 1]. \mforall{}[m4:\mBbbN{}m3 + 1].
(partial\_ap(partial\_ap\_gen(g;m1;m2;m3);m3;m4) \msim{} partial\_ap\_gen(g;m1;m2;m4))
Date html generated:
2016_05_15-PM-02_12_00
Last ObjectModification:
2016_01_15-PM-10_20_34
Theory : untyped!computation
Home
Index