Nuprl Lemma : add-add-zero-in-top
∀[a,b:Top]. ((a + b) + 0 ~ a + b)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
false: False
Lemmas referenced :
value-type-has-value,
int-value-type,
equal_wf,
add-zero,
exception-not-value,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueAdd,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lambdaFormation,
extract_by_obid,
isectElimination,
intEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
sqleReflexivity,
addExceptionCases,
axiomSqleEquality,
natural_numberEquality,
voidElimination,
exceptionSqequal,
addEquality,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[a,b:Top]. ((a + b) + 0 \msim{} a + b)
Date html generated:
2017_10_01-AM-08_43_29
Last ObjectModification:
2017_07_26-PM-04_29_48
Theory : untyped!computation
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