Nuprl Lemma : modulus_functionality_wrt_eqmod
∀[m:ℕ+]. ∀[x,y:ℤ]. (x mod m) = (y mod m) ∈ ℤ supposing x ≡ y mod m
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
modulus: a mod n,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+
Lemmas referenced :
modulus-equal-iff-eqmod,
eqmod_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
hypothesis,
isectElimination,
setElimination,
rename,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[m:\mBbbN{}\msupplus{}]. \mforall{}[x,y:\mBbbZ{}]. (x mod m) = (y mod m) supposing x \mequiv{} y mod m
Date html generated:
2016_05_14-PM-04_23_04
Last ObjectModification:
2015_12_26-PM-08_18_45
Theory : num_thy_1
Home
Index