Nuprl Lemma : seq-append0
∀[n:ℕ]. ∀[s,t:Top]. (seq-append(n;0;s;t) ~ seq-normalize(n;s))
Proof
Definitions occuring in Statement :
seq-normalize: seq-normalize(n;s),
seq-append: seq-append(n;m;s1;s2),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
seq-normalize: seq-normalize(n;s),
seq-append: seq-append(n;m;s1;s2),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(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,
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
top_wf,
nat_wf,
less_than_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
not-lt-2,
less-iff-le,
condition-implies-le,
minus-add,
base_wf,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-commutes,
add-associates,
zero-add,
add_functionality_wrt_le,
le-add-cancel,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
equal-wf-base,
less_sqequal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
thin,
sqequalHypSubstitution,
hypothesis,
sqequalAxiom,
extract_by_obid,
isect_memberEquality,
isectElimination,
hypothesisEquality,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
lambdaFormation,
productElimination,
independent_pairFormation,
addEquality,
natural_numberEquality,
unionElimination,
equalityElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
lessCases,
voidElimination,
voidEquality,
imageMemberEquality,
imageElimination,
independent_functionElimination,
dependent_functionElimination,
applyEquality,
lambdaEquality,
intEquality,
minusEquality,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
impliesFunctionality,
productEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[s,t:Top]. (seq-append(n;0;s;t) \msim{} seq-normalize(n;s))
Date html generated:
2017_04_14-AM-07_27_07
Last ObjectModification:
2017_02_27-PM-02_56_22
Theory : bar-induction
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