Nuprl Lemma : grp_inv_id
∀[g:IGroup]. ((~ e) = e ∈ |g|)
Proof
Definitions occuring in Statement :
igrp: IGroup,
grp_inv: ~,
grp_id: e,
grp_car: |g|,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
igrp: IGroup,
imon: IMonoid,
and: P ∧ Q,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
igrp_wf,
equal_wf,
squash_wf,
true_wf,
grp_car_wf,
grp_inv_wf,
grp_id_wf,
grp_inverse,
iff_weakening_equal,
mon_ident
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
setElimination,
rename,
because_Cache,
productElimination,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[g:IGroup]. ((\msim{} e) = e)
Date html generated:
2017_10_01-AM-08_13_35
Last ObjectModification:
2017_02_28-PM-01_57_51
Theory : groups_1
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