Nuprl Lemma : massoc_functionality_wrt_massoc
∀g:IAbMonoid. ∀a,a',b,b':|g|. ((a ~ b) ⇒ (a' ~ b') ⇒ (a ~ a' ⇐⇒ b ~ b'))
Proof
Definitions occuring in Statement :
massoc: a ~ b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
iabmonoid_wf,
equiv_rel_self_functionality,
grp_car_wf,
massoc_wf,
massoc_equiv_rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}a,a',b,b':|g|. ((a \msim{} b) {}\mRightarrow{} (a' \msim{} b') {}\mRightarrow{} (a \msim{} a' \mLeftarrow{}{}\mRightarrow{} b \msim{} b'))
Date html generated:
2016_05_16-AM-07_43_41
Last ObjectModification:
2015_12_28-PM-05_54_23
Theory : factor_1
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