Nuprl Lemma : int_is_mono
∀[x:ℤ]. ∀[y:Base]. y ≤ x supposing x ≤ y
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
has-value: (a)↓,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
eq_int: (i =z j),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
false: False,
guard: {T},
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
not: ¬A
Lemmas referenced :
has-value_wf_base,
is-exception_wf,
istype-sqle,
int_subtype_base,
istype-base,
istype-int,
has-value-monotonic,
value-type-has-value,
int-value-type,
add-subtract-cancel,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
not-bfalse-sqle-btrue,
subtract-add-cancel,
subtract_wf,
exception-not-value2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
divergentSqle,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
axiomSqleEquality,
hypothesisEquality,
applyEquality,
sqequalRule,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
sqleRule,
sqleReflexivity,
baseClosed,
baseApply,
closedConclusion,
independent_isectElimination,
intEquality,
addEquality,
natural_numberEquality,
callbyvalueAdd,
productElimination,
equalityTransitivity,
equalitySymmetry,
Error :lambdaFormation_alt,
dependent_functionElimination,
Error :equalityIstype,
independent_functionElimination,
intWeakElimination,
rename,
Error :lambdaEquality_alt,
axiomEquality,
unionElimination,
equalityElimination,
voidElimination,
Error :dependent_pairFormation_alt,
promote_hyp,
instantiate,
cumulativity,
exceptionSqequal
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y:Base]. y \mleq{} x supposing x \mleq{} y
Date html generated:
2019_06_20-PM-00_25_57
Last ObjectModification:
2018_11_28-AM-10_06_28
Theory : int_1
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