Nuprl Lemma : eqmod_fun
∀m,a,a',b,b':ℤ. ((a ≡ a' mod m) ⇒ (b ≡ b' mod m) ⇒ (a ≡ b mod m ⇐⇒ a' ≡ b' mod m))
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
eqmod_wf,
istype-int,
eqmod_inversion,
eqmod_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
independent_pairFormation,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
dependent_functionElimination,
independent_functionElimination,
because_Cache
Latex:
\mforall{}m,a,a',b,b':\mBbbZ{}. ((a \mequiv{} a' mod m) {}\mRightarrow{} (b \mequiv{} b' mod m) {}\mRightarrow{} (a \mequiv{} b mod m \mLeftarrow{}{}\mRightarrow{} a' \mequiv{} b' mod m))
Date html generated:
2019_06_20-PM-02_24_21
Last ObjectModification:
2018_10_03-AM-00_13_14
Theory : num_thy_1
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