Nuprl Lemma : grp_op_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,
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iabmonoid: IAbMonoid,
grp_op: *,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
iabmonoid: IAbMonoid,
imon: IMonoid,
uall: ∀[x:A]. B[x],
massoc: a ~ b,
symmetrize: Symmetrize(x,y.R[x; y];a;b),
and: P ∧ Q
Lemmas referenced :
massoc_wf,
grp_car_wf,
iabmonoid_wf,
grp_op_ap2_functionality_wrt_mdivides
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isectElimination,
productElimination,
independent_pairFormation,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}a,a',b,b':|g|. ((a \msim{} b) {}\mRightarrow{} (a' \msim{} b') {}\mRightarrow{} ((a * a') \msim{} (b * b')))
Date html generated:
2016_05_16-AM-07_43_39
Last ObjectModification:
2015_12_28-PM-05_54_29
Theory : factor_1
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