Nuprl Lemma : simple-cbva-seq-list
∀F:Top. ∀L1,L2:ℤ ⟶ Base. ∀m:ℕ. ((∀j:ℕm + 1. (L1 j ~ L2 j)) ⇒ (simple-cbva-seq(L1;F;m) ~ simple-cbva-seq(L2;F;m)))
Proof
Definitions occuring in Statement :
simple-cbva-seq: simple-cbva-seq(L;F;m),
int_seg: {i..j-},
nat: ℕ,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
simple-cbva-seq: simple-cbva-seq(L;F;m),
cbva-seq: cbva-seq(L;F;m),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
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 ,
sq_type: SQType(T),
guard: {T},
callbyvalueall-seq: callbyvalueall-seq(L;G;F;n;m),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
prop: ℙ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
int_upper: {i...},
decidable: Dec(P),
int_seg: {i..j-},
lelt: i ≤ j < k
Lemmas referenced :
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
subtype_base_sq,
int_subtype_base,
btrue_wf,
assert_of_le_int,
eqff_to_assert,
le_int_wf,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
le_wf,
nat_properties,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
set_subtype_base,
neg_assert_of_eq_int,
upper_subtype_nat,
istype-false,
nequal-le-implies,
zero-add,
int_upper_properties,
decidable__le,
intformand_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__equal_int,
itermAdd_wf,
int_term_value_add_lemma,
intformless_wf,
int_formula_prop_less_lemma,
ge_wf,
istype-less_than,
int_seg_wf,
istype-sqequal,
subtract-1-ge-0,
decidable__lt,
subtype_rel_self,
nat_wf,
istype-base,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
natural_numberEquality,
inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
instantiate,
cumulativity,
intEquality,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation_alt,
equalityIsType2,
hypothesisEquality,
baseClosed,
promote_hyp,
voidElimination,
universeIsType,
approximateComputation,
lambdaEquality_alt,
isect_memberEquality_alt,
equalityIsType1,
baseApply,
closedConclusion,
applyEquality,
hypothesis_subsumption,
independent_pairFormation,
dependent_set_memberEquality_alt,
applyLambdaEquality,
int_eqEquality,
equalityIsType4,
intWeakElimination,
axiomSqEquality,
functionIsTypeImplies,
addEquality,
functionIsType,
productIsType
Latex:
\mforall{}F:Top. \mforall{}L1,L2:\mBbbZ{} {}\mrightarrow{} Base. \mforall{}m:\mBbbN{}.
((\mforall{}j:\mBbbN{}m + 1. (L1 j \msim{} L2 j)) {}\mRightarrow{} (simple-cbva-seq(L1;F;m) \msim{} simple-cbva-seq(L2;F;m)))
Date html generated:
2019_10_15-AM-10_59_03
Last ObjectModification:
2018_10_17-AM-11_53_39
Theory : untyped!computation
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