Nuprl Lemma : seq-append-normalize
∀[n,m:ℕ]. ∀[s1,s2:Top]. (seq-append(n;m;s1;seq-normalize(m;s2)) ~ seq-append(n;m;s1;s2))
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,
sqequal: s ~ t
Definitions unfolded in proof :
seq-append: seq-append(n;m;s1;s2),
seq-normalize: seq-normalize(n;s),
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
all: ∀x:A. B[x],
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,
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,
prop: ℙ,
subtract: n - m,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
le: A ≤ B,
has-value: (a)↓,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
istype-void,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
less_than_wf,
iff_weakening_uiff,
assert_of_bnot,
subtract_wf,
add-commutes,
minus-one-mul,
less-iff-le,
add_functionality_wrt_le,
le_reflexive,
minus-one-mul-top,
add-associates,
minus-add,
one-mul,
add-swap,
add-mul-special,
two-mul,
mul-distributes-right,
zero-mul,
add-zero,
zero-add,
not-lt-2,
mul-associates,
omega-shadow,
mul-distributes,
mul-swap,
le-add-cancel,
top_wf,
nat_wf,
nat_properties,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
has-value_wf_base,
is-exception_wf,
bottom-sqle
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
thin,
Error :lambdaFormation_alt,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
setElimination,
rename,
hypothesisEquality,
Error :inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
because_Cache,
lessCases,
Error :isect_memberFormation_alt,
axiomSqEquality,
Error :isect_memberEquality_alt,
Error :universeIsType,
independent_pairFormation,
voidElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
imageElimination,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :equalityIsType1,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
addEquality,
Error :equalityIsType4,
intEquality,
multiplyEquality,
applyEquality,
Error :lambdaEquality_alt,
minusEquality,
Error :dependent_set_memberEquality_alt,
sqequalSqle,
divergentSqle,
callbyvalueLess,
baseApply,
closedConclusion,
sqleReflexivity,
lessExceptionCases,
axiomSqleEquality,
exceptionSqequal
Latex:
\mforall{}[n,m:\mBbbN{}]. \mforall{}[s1,s2:Top]. (seq-append(n;m;s1;seq-normalize(m;s2)) \msim{} seq-append(n;m;s1;s2))
Date html generated:
2019_06_20-AM-11_28_38
Last ObjectModification:
2018_09_28-PM-10_42_46
Theory : bar-induction
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