Nuprl Lemma : sqeq-copath4
∀[a,b,c,m:Top].
(λx.if (x) < (m) then if (x) < (m) then a[x] else b[x] else c[x] ~ λx.if (x) < (m) then a[x] else c[x])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
less: if (a) < (b) then c else d,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
prop: ℙ,
false: False,
not: ¬A,
squash: ↓T,
true: True,
top: Top,
less_than': less_than'(a;b),
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
has-value: (a)↓
Lemmas referenced :
top_wf,
is-exception_wf,
has-value_wf_base,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
less_than_wf,
assert_of_lt_int,
eqtt_to_assert,
bool_wf,
lt_int_wf
Rules used in proof :
isect_memberEquality,
axiomSqEquality,
isect_memberFormation,
because_Cache,
sqleReflexivity,
hypothesis,
hypothesisEquality,
baseClosed,
closedConclusion,
baseApply,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
divergentSqle,
thin,
sqleRule,
cut,
sqequalSqle,
sqequalRule,
cumulativity,
instantiate,
dependent_functionElimination,
promote_hyp,
dependent_pairFormation,
independent_functionElimination,
imageElimination,
imageMemberEquality,
natural_numberEquality,
voidEquality,
voidElimination,
independent_pairFormation,
lessCases,
independent_isectElimination,
equalitySymmetry,
equalityTransitivity,
equalityElimination,
unionElimination,
lambdaFormation,
productElimination,
callbyvalueLess,
exceptionSqequal,
axiomSqleEquality,
lessExceptionCases,
exceptionLess
Latex:
\mforall{}[a,b,c,m:Top].
(\mlambda{}x.if (x) < (m) then if (x) < (m) then a[x] else b[x] else c[x] \msim{} \mlambda{}x.if (x) < (m)
then a[x]
else c[x])
Date html generated:
2019_06_20-PM-01_12_09
Last ObjectModification:
2019_01_02-PM-01_35_38
Theory : co-recursion-2
Home
Index