Nuprl Lemma : partial_ap_is_gen
∀[g:Top]. ∀[m,n:ℕ]. (partial_ap(g;m;n) ~ partial_ap_gen(g;m;0;n))
Proof
Definitions occuring in Statement :
partial_ap: partial_ap(g;n;m),
partial_ap_gen: partial_ap_gen(g;n;s;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
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),
uimplies: b supposing a,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
mk_lambdas: mk_lambdas(F;m)
Lemmas referenced :
top_wf,
nat_wf,
primrec0_lemma,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
itermVar_wf,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_properties,
int_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[g:Top]. \mforall{}[m,n:\mBbbN{}]. (partial\_ap(g;m;n) \msim{} partial\_ap\_gen(g;m;0;n))
Date html generated:
2016_05_15-PM-02_12_06
Last ObjectModification:
2016_01_15-PM-10_20_15
Theory : untyped!computation
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