Nuprl Lemma : partial_ap_compose
∀[g:Top]. ∀[m1:ℕ]. ∀[m2:ℕm1 + 1]. ∀[m3:ℕm2 + 1]. (partial_ap(partial_ap(g;m1;m2);m2;m3) ~ partial_ap(g;m1;m3))
Proof
Definitions occuring in Statement :
partial_ap: partial_ap(g;n;m),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
guard: {T},
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],
top: Top,
less_than: a < b
Lemmas referenced :
top_wf,
nat_wf,
int_seg_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_properties,
int_seg_properties,
partial_ap_of_partial_ap_gen,
false_wf,
int_seg_subtype_nat,
partial_ap_is_gen
Rules used in proof :
sqequalSubstitution,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
natural_numberEquality,
addEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
hypothesis,
because_Cache,
dependent_set_memberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[g:Top]. \mforall{}[m1:\mBbbN{}]. \mforall{}[m2:\mBbbN{}m1 + 1]. \mforall{}[m3:\mBbbN{}m2 + 1].
(partial\_ap(partial\_ap(g;m1;m2);m2;m3) \msim{} partial\_ap(g;m1;m3))
Date html generated:
2016_05_15-PM-02_12_09
Last ObjectModification:
2016_01_15-PM-10_20_39
Theory : untyped!computation
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