Nuprl Lemma : firstn-mklist1
∀[m,n:ℕ]. ∀[f:ℕm ⟶ Top]. ((n ≤ m) ⇒ (firstn(n;mklist(m;f)) ~ mklist(n;f)))
Proof
Definitions occuring in Statement :
mklist: mklist(n;f),
firstn: firstn(n;as),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
le: A ≤ B,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Lemmas referenced :
le_wf,
int_seg_wf,
top_wf,
nat_wf,
firstn-mklist,
subtype_base_sq,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
imin_unfold,
iff_weakening_equal,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
sqequalAxiom,
because_Cache,
functionEquality,
natural_numberEquality,
isect_memberEquality,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
applyEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
unionElimination,
equalityElimination,
dependent_pairFormation,
promote_hyp,
voidElimination
Latex:
\mforall{}[m,n:\mBbbN{}]. \mforall{}[f:\mBbbN{}m {}\mrightarrow{} Top]. ((n \mleq{} m) {}\mRightarrow{} (firstn(n;mklist(m;f)) \msim{} mklist(n;f)))
Date html generated:
2017_04_17-AM-08_01_41
Last ObjectModification:
2017_02_27-PM-04_31_53
Theory : list_1
Home
Index