Nuprl Lemma : seq-append0-left
∀[t:Top]. ∀[m:ℕ]. ∀[f:ℕm ⟶ ℕ]. (seq-append(0;m;t;f) = f ∈ (ℕm ⟶ ℕ))
Proof
Definitions occuring in Statement :
seq-append: seq-append(n;m;s1;s2),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
seq-append: seq-append(n;m;s1;s2),
int_seg: {i..j-},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
less_than: a < b,
less_than': less_than'(a;b),
top: Top,
true: True,
squash: ↓T,
not: ¬A,
false: False,
prop: ℙ,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
le: A ≤ B,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
subtract: n - m
Lemmas referenced :
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
top_wf,
less_than_wf,
int_seg_properties,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
lelt_wf,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
minus-zero,
add-zero,
intformnot_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_term_value_add_lemma,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
because_Cache,
lessCases,
sqequalAxiom,
isect_memberEquality,
independent_pairFormation,
voidElimination,
voidEquality,
imageMemberEquality,
baseClosed,
imageElimination,
independent_functionElimination,
dependent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
applyEquality,
dependent_set_memberEquality,
promote_hyp,
instantiate,
cumulativity,
addEquality,
functionEquality,
axiomEquality
Latex:
\mforall{}[t:Top]. \mforall{}[m:\mBbbN{}]. \mforall{}[f:\mBbbN{}m {}\mrightarrow{} \mBbbN{}]. (seq-append(0;m;t;f) = f)
Date html generated:
2017_04_17-AM-10_02_51
Last ObjectModification:
2017_02_27-PM-05_54_24
Theory : continuity
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