Nuprl Lemma : add-inverse
∀[x:ℤ]. (x + (-x) ~ 0)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
add: n + m,
minus: -n,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_type: SQType(T),
uimplies: b supposing a
Lemmas referenced :
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
addInverse,
hypothesisEquality,
hypothesis,
axiomSqEquality,
Error :universeIsType,
intEquality,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
dependent_functionElimination,
independent_isectElimination,
cumulativity,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
instantiate,
thin
Latex:
\mforall{}[x:\mBbbZ{}]. (x + (-x) \msim{} 0)
Date html generated:
2019_06_20-AM-11_22_03
Last ObjectModification:
2018_10_15-PM-03_13_16
Theory : arithmetic
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