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
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