Nuprl Lemma : int_eq-sqle-lemma1
∀[x:Top]. ∀[y:ℤ]. (if x=y then x else ⊥ ≤ x)
Proof
Definitions occuring in Statement :
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
int_eq: if a=b then c else d,
int: ℤ,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
subtype_rel: A ⊆r B,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
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,
false: False,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
int_subtype_base,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
has-value_wf_base,
is-exception_wf,
eqff_to_assert,
bool_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
iff_weakening_uiff,
assert_of_bnot,
istype-assert,
istype-void,
bottom-sqle,
exception-not-value,
value-type-has-value,
int-value-type,
istype-int,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqleRule,
thin,
divergentSqle,
callbyvalueIntEq,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
extract_by_obid,
productElimination,
isectElimination,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
equalityElimination,
because_Cache,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
int_eqReduceTrueSq,
sqleReflexivity,
Error :dependent_pairFormation_alt,
Error :equalityIsType4,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
intEquality,
independent_pairFormation,
Error :functionIsType,
int_eqReduceFalseSq,
Error :isect_memberEquality_alt,
Error :equalityIsType1,
int_eqExceptionCases,
axiomSqleEquality,
exceptionSqequal,
Error :isectIsTypeImplies
Latex:
\mforall{}[x:Top]. \mforall{}[y:\mBbbZ{}]. (if x=y then x else \mbot{} \mleq{} x)
Date html generated:
2019_06_20-AM-11_27_24
Last ObjectModification:
2018_10_27-AM-11_14_36
Theory : call!by!value_2
Home
Index