Nuprl Lemma : int-subtype-int_mod
∀[n:ℤ]. (ℤ ⊆r ℤ_n)
Proof
Definitions occuring in Statement :
int_mod: ℤ_n,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
int_mod: ℤ_n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_quotient,
eqmod_wf,
eqmod_equiv_rel
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
axiomEquality
Latex:
\mforall{}[n:\mBbbZ{}]. (\mBbbZ{} \msubseteq{}r \mBbbZ{}\_n)
Date html generated:
2016_05_14-PM-09_25_59
Last ObjectModification:
2015_12_26-PM-08_02_39
Theory : num_thy_1
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