Nuprl Lemma : seq-normalize0
seq-normalize(0;λm.⊥) ~ λm.eval x = m in
⊥
Proof
Definitions occuring in Statement :
seq-normalize: seq-normalize(n;s),
bottom: ⊥,
callbyvalue: callbyvalue,
lambda: λx.A[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
seq-normalize: seq-normalize(n;s),
has-value: (a)↓,
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
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,
prop: ℙ,
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 :
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
top_wf,
less_than_wf,
bottom-sqle,
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,
exception-not-value,
value-type-has-value,
int-value-type,
has-value_wf_base,
is-exception_wf,
bottom_diverge,
exception-not-bottom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
sqequalSqle,
cut,
divergentSqle,
callbyvalueLess,
sqequalHypSubstitution,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
thin,
productElimination,
introduction,
extract_by_obid,
isectElimination,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
lessCases,
isect_memberFormation,
sqequalAxiom,
isect_memberEquality,
independent_pairFormation,
voidElimination,
voidEquality,
natural_numberEquality,
imageMemberEquality,
imageElimination,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
impliesFunctionality,
lessExceptionCases,
axiomSqleEquality,
intEquality,
exceptionSqequal,
sqleReflexivity,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases
Latex:
seq-normalize(0;\mlambda{}m.\mbot{}) \msim{} \mlambda{}m.eval x = m in
\mbot{}
Date html generated:
2017_04_14-AM-07_26_50
Last ObjectModification:
2017_02_27-PM-02_56_07
Theory : bar-induction
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