Nuprl Lemma : zero-add-sqle
∀[x:Top]. (0 + x ≤ x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x]
,
top: Top
,
add: n + m
,
natural_number: $n
,
sqle: s ≤ t
Definitions unfolded in proof :
false: False
,
implies: P
⇒ Q
,
uimplies: b supposing a
,
and: P ∧ Q
,
has-value: (a)↓
,
member: t ∈ T
,
uall: ∀[x:A]. B[x]
Lemmas referenced :
is-exception_wf,
has-value_wf_base,
zero-add,
exception-not-value,
value-type-has-value,
int-value-type,
top_wf
Rules used in proof :
voidElimination,
independent_functionElimination,
natural_numberEquality,
intEquality,
independent_isectElimination,
isectElimination,
lemma_by_obid,
sqleReflexivity,
exceptionSqequal,
axiomSqleEquality,
addExceptionCases,
productElimination,
hypothesisEquality,
closedConclusion,
baseApply,
sqequalRule,
baseClosed,
hypothesis,
sqequalHypSubstitution,
callbyvalueAdd,
divergentSqle,
thin,
sqleRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
equalitySymmetry,
equalityTransitivity,
extract_by_obid
Latex:
\mforall{}[x:Top]. (0 + x \mleq{} x)
Date html generated:
2018_05_21-PM-00_01_43
Last ObjectModification:
2017_11_21-AM-11_24_20
Theory : arithmetic
Home
Index