Nuprl Lemma : simple-cbva-seq-sqequal-n
∀L:Top. ∀F1,F2:Base. ∀m,n:ℕ.
(((m ≤ (n + 2)) ⇒ (F1 ~(n - m) + 2 F2)) ⇒ (simple-cbva-seq(L;F1;m) ~n simple-cbva-seq(L;F2;m)))
Proof
Definitions occuring in Statement :
simple-cbva-seq: simple-cbva-seq(L;F;m),
nat: ℕ,
top: Top,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtract: n - m,
add: n + m,
natural_number: $n,
base: Base,
sqequal_n: s ~n t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
simple-cbva-seq: simple-cbva-seq(L;F;m),
cbva-seq: cbva-seq(L;F;m),
uall: ∀[x:A]. B[x],
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 ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
ge: i ≥ j ,
int_upper: {i...},
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
callbyvalueall-seq: callbyvalueall-seq(L;G;F;n;m),
le_int: i ≤z j,
lt_int: i <z j,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
callbyvalueall: callbyvalueall
Lemmas referenced :
decidable__lt,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
false_wf,
le_wf,
nat_properties,
nequal-le-implies,
zero-add,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
sqequal_n_wf,
subtract_wf,
decidable__le,
itermSubtract_wf,
int_term_value_subtract_lemma,
nat_wf,
base_wf,
top_wf,
int_subtype_base,
btrue_wf,
assert_of_le_int,
intformeq_wf,
int_formula_prop_eq_lemma,
decidable__equal_int,
sqequal_n_add,
add-subtract-cancel,
le_int_wf,
int_upper_properties,
less_than_wf,
all_wf,
set_subtype_base,
set_wf,
primrec-wf2,
mk_lambdas-sqequal-n2,
general_arith_equation1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequal_n rule,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
natural_numberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
unionElimination,
promote_hyp,
isectElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
dependent_pairFormation,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
hypothesis_subsumption,
dependent_set_memberEquality,
independent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
computeAll,
sqequalZero,
sqequalnReflexivity,
functionEquality,
baseClosed,
applyLambdaEquality,
imageElimination,
baseApply,
closedConclusion,
applyEquality
Latex:
\mforall{}L:Top. \mforall{}F1,F2:Base. \mforall{}m,n:\mBbbN{}.
(((m \mleq{} (n + 2)) {}\mRightarrow{} (F1 \msim{}(n - m) + 2 F2)) {}\mRightarrow{} (simple-cbva-seq(L;F1;m) \msim{}n simple-cbva-seq(L;F2;m)))
Date html generated:
2017_10_01-AM-08_43_15
Last ObjectModification:
2017_07_26-PM-04_29_38
Theory : untyped!computation
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