Nuprl Lemma : abdgrp_properties
∀[g:AbDGrp]. IsEqFun(|g|;=b)
Proof
Definitions occuring in Statement :
abdgrp: AbDGrp,
grp_eq: =b,
grp_car: |g|,
eqfun_p: IsEqFun(T;eq),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
abdgrp: AbDGrp,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
eqfun_p: IsEqFun(T;eq),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
infix_ap: x f y
Lemmas referenced :
abdgrp_wf,
equal_wf,
assert_witness,
assert_wf,
grp_eq_wf,
grp_car_wf,
sq_stable__eqfun_p
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
productElimination,
independent_pairEquality,
axiomEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[g:AbDGrp]. IsEqFun(|g|;=\msubb{})
Date html generated:
2016_05_15-PM-00_09_41
Last ObjectModification:
2016_01_15-PM-11_06_08
Theory : groups_1
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