Nuprl Lemma : mul-commutes
∀[x:ℤ]. ∀[y:Top]. (x * y ~ y * x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
multiply: n * m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
false: False,
top: Top,
guard: {T},
implies: P ⇒ Q,
sq_type: SQType(T),
uimplies: b supposing a,
and: P ∧ Q,
subtype_rel: A ⊆r B,
has-value: (a)↓,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_subtype_base,
subtype_base_sq,
has-value_wf_base,
is-exception_wf,
int-mul-exception,
exception-not-value,
value-type-has-value,
int-value-type,
top_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
multiplyCommutative,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
Error :universeIsType,
intEquality,
axiomSqEquality,
voidEquality,
voidElimination,
isect_memberEquality,
exceptionSqequal,
axiomSqleEquality,
multiplyExceptionCases,
because_Cache,
sqleReflexivity,
independent_functionElimination,
independent_isectElimination,
cumulativity,
isectElimination,
instantiate,
equalitySymmetry,
equalityTransitivity,
dependent_functionElimination,
productElimination,
lemma_by_obid,
applyEquality,
baseClosed,
closedConclusion,
baseApply,
sqequalRule,
sqequalHypSubstitution,
callbyvalueMultiply,
divergentSqle,
thin,
sqleRule,
sqequalSqle,
introduction,
isect_memberFormation
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y:Top]. (x * y \msim{} y * x)
Date html generated:
2019_06_20-AM-11_22_04
Last ObjectModification:
2018_10_15-PM-03_04_51
Theory : arithmetic
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