Nuprl Lemma : subtract_functionality_wrt_eqmod
∀m,a,a',b,b':ℤ. ((a ≡ a' mod m) ⇒ (b ≡ b' mod m) ⇒ ((a - b) ≡ (a' - b') mod m))
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtract: n - m,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
eqmod_wf,
subtract_wf,
eqmod_functionality_wrt_eqmod,
subtract-elim,
add_functionality_wrt_eqmod,
minus_functionality_wrt_eqmod,
eqmod_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
addEquality,
minusEquality,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
independent_functionElimination,
productElimination
Latex:
\mforall{}m,a,a',b,b':\mBbbZ{}. ((a \mequiv{} a' mod m) {}\mRightarrow{} (b \mequiv{} b' mod m) {}\mRightarrow{} ((a - b) \mequiv{} (a' - b') mod m))
Date html generated:
2016_05_14-PM-04_22_22
Last ObjectModification:
2015_12_26-PM-08_18_23
Theory : num_thy_1
Home
Index