Nuprl Lemma : perm_grp_inverse
∀[T:Type]. ∀[a:Perm(T)]. ((a O inv_perm(a) = id_perm() ∈ Perm(T)) ∧ (inv_perm(a) O a = id_perm() ∈ Perm(T)))
Proof
Definitions occuring in Statement :
comp_perm: comp_perm,
inv_perm: inv_perm(p),
id_perm: id_perm(),
perm: Perm(T),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
perm_igrp: perm_igrp(T),
mk_igrp: mk_igrp(T;op;id;inv),
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
grp_inv: ~,
grp_id: e,
infix_ap: x f y,
and: P ∧ Q,
all: ∀x:A. B[x]
Lemmas referenced :
grp_inverse,
perm_igrp_wf,
perm_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
productElimination,
independent_pairEquality,
axiomEquality,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:Perm(T)]. ((a O inv\_perm(a) = id\_perm()) \mwedge{} (inv\_perm(a) O a = id\_perm()))
Date html generated:
2016_05_16-AM-07_29_20
Last ObjectModification:
2015_12_28-PM-05_36_30
Theory : perms_1
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