Nuprl Lemma : add-commutes
∀[x:ℤ]. ∀[y:Top]. (x + y ~ y + x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
has-value: (a)↓,
subtype_rel: A ⊆r B,
and: P ∧ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
top: Top,
false: False
Lemmas referenced :
int_subtype_base,
subtype_base_sq,
has-value_wf_base,
is-exception_wf,
int-add-exception,
exception-not-value,
value-type-has-value,
int-value-type,
top_wf
Rules used in proof :
cut,
intEquality,
hypothesis,
hypothesisEquality,
addCommutative,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
isect_memberFormation,
introduction,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueAdd,
sqequalHypSubstitution,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
extract_by_obid,
productElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
isectElimination,
cumulativity,
independent_isectElimination,
independent_functionElimination,
sqleReflexivity,
because_Cache,
addExceptionCases,
axiomSqleEquality,
exceptionSqequal,
isect_memberEquality,
voidElimination,
voidEquality,
axiomSqEquality
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y:Top]. (x + y \msim{} y + x)
Date html generated:
2019_06_20-AM-11_22_02
Last ObjectModification:
2018_09_24-PM-00_40_48
Theory : arithmetic
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