Nuprl Lemma : multiply_one_int_mod
∀[n:ℤ]. ∀[x:ℤ_n]. ((x * 1) = x ∈ ℤ_n)
Proof
Definitions occuring in Statement :
int_mod: ℤ_n,
uall: ∀[x:A]. B[x],
multiply: n * m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_mod: ℤ_n,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
eqmod_wf,
equal_wf,
equal-wf-base,
int_mod_wf,
quotient-member-eq,
eqmod_equiv_rel,
mul-one
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
hypothesis,
equalitySymmetry,
intEquality,
lambdaFormation,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
productEquality,
isect_memberEquality,
axiomEquality,
lambdaEquality,
independent_isectElimination,
multiplyEquality,
natural_numberEquality
Latex:
\mforall{}[n:\mBbbZ{}]. \mforall{}[x:\mBbbZ{}\_n]. ((x * 1) = x)
Date html generated:
2017_04_17-AM-09_48_07
Last ObjectModification:
2017_02_27-PM-05_44_52
Theory : num_thy_1
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