Nuprl Lemma : fun_exp_add_sq
∀[n,m:ℕ]. ∀[f,i:Top]. (f^n + m i ~ f^n (f^m i))
Proof
Definitions occuring in Statement :
fun_exp: f^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
add: n + m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
sq_type: SQType(T),
sq_stable: SqStable(P),
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b,
compose: f o g
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
top_wf,
nat_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
fun_exp0_lemma,
subtract-add-cancel,
subtype_base_sq,
int_subtype_base,
fun_exp_unroll,
not-le-2,
sq_stable__le,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
le_antisymmetry_iff,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
add-subtract-cancel,
add_nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
sqequalAxiom,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
applyEquality,
voidEquality,
intEquality,
minusEquality,
because_Cache,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed,
imageElimination,
equalityElimination,
dependent_pairFormation,
promote_hyp
Latex:
\mforall{}[n,m:\mBbbN{}]. \mforall{}[f,i:Top]. (f\^{}n + m i \msim{} f\^{}n (f\^{}m i))
Date html generated:
2017_04_14-AM-07_34_53
Last ObjectModification:
2017_02_27-PM-03_07_50
Theory : fun_1
Home
Index