Nuprl Lemma : partial_ap_of_partial_ap_gen1
∀[g:Top]. ∀[m1,m2:ℕ].
(partial_ap(partial_ap_gen(g;(m1 + m2) + 1;m1;m2 + 1);m2 + 1;m2) ~ partial_ap_gen(g;(m1 + m2) + 1;m1;m2))
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,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
ge: i ≥ j ,
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,
top: Top,
and: P ∧ Q,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B
Lemmas referenced :
top_wf,
nat_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
lelt_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
partial_ap_of_partial_ap_gen
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
productElimination,
because_Cache,
sqequalAxiom
Latex:
\mforall{}[g:Top]. \mforall{}[m1,m2:\mBbbN{}].
(partial\_ap(partial\_ap\_gen(g;(m1 + m2) + 1;m1;m2 + 1);m2 + 1;m2) \msim{} partial\_ap\_gen(g;(m1 + m2)
+ 1;m1;m2))
Date html generated:
2016_05_15-PM-02_12_03
Last ObjectModification:
2016_01_15-PM-10_20_29
Theory : untyped!computation
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