Nuprl Lemma : grp_eq_sym
∀[g:DMon]. ∀[a,b:|g|]. a =b b = b =b a
Proof
Definitions occuring in Statement :
dmon: DMon,
grp_eq: =b,
grp_car: |g|,
bool: 𝔹,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
infix_ap: x f y,
dmon: DMon,
mon: Mon,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q)
Lemmas referenced :
iff_imp_equal_bool,
grp_eq_wf,
equal_wf,
grp_car_wf,
assert_of_mon_eq,
assert_wf,
iff_wf,
dmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
equalitySymmetry,
addLevel,
productElimination,
impliesFunctionality,
because_Cache,
sqequalRule,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[g:DMon]. \mforall{}[a,b:|g|]. a =\msubb{} b = b =\msubb{} a
Date html generated:
2016_05_15-PM-00_07_08
Last ObjectModification:
2015_12_26-PM-11_46_58
Theory : groups_1
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