Nuprl Lemma : assoced_functionality_wrt_assoced
∀a,b,a',b':ℤ. ((a ~ a') ⇒ (b ~ b') ⇒ (a ~ b ⇐⇒ a' ~ b'))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
equiv_rel_self_functionality,
assoced_wf,
istype-int,
assoced_equiv_rel
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
intEquality,
sqequalRule,
Error :lambdaEquality_alt,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
independent_functionElimination
Latex:
\mforall{}a,b,a',b':\mBbbZ{}. ((a \msim{} a') {}\mRightarrow{} (b \msim{} b') {}\mRightarrow{} (a \msim{} b \mLeftarrow{}{}\mRightarrow{} a' \msim{} b'))
Date html generated:
2019_06_20-PM-02_21_04
Last ObjectModification:
2018_10_03-AM-10_23_40
Theory : num_thy_1
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