Nuprl Lemma : decidable__mon_eq
∀g:DMon. ∀a,b:|g|. Dec(a = b ∈ |g|)
Proof
Definitions occuring in Statement :
dmon: DMon,
grp_car: |g|,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
dmon: DMon,
mon: Mon,
eqfun_p: IsEqFun(T;eq),
infix_ap: x f y,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
dmon_properties,
grp_car_wf,
dmon_wf,
decidable_functionality,
equal_wf,
assert_wf,
grp_eq_wf,
iff_weakening_uiff,
decidable__assert
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
applyEquality,
independent_functionElimination,
because_Cache,
productElimination,
independent_pairFormation,
dependent_functionElimination
Latex:
\mforall{}g:DMon. \mforall{}a,b:|g|. Dec(a = b)
Date html generated:
2016_05_15-PM-00_07_06
Last ObjectModification:
2015_12_26-PM-11_46_56
Theory : groups_1
Home
Index