Nuprl Lemma : perm_grp_inv_thru_op
∀[T:Type]. ∀[a,b:Perm(T)]. (inv_perm(a O b) = inv_perm(b) O inv_perm(a) ∈ Perm(T))
Proof
Definitions occuring in Statement :
comp_perm: comp_perm,
inv_perm: inv_perm(p),
perm: Perm(T),
uall: ∀[x:A]. B[x],
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_inv: ~,
pi2: snd(t),
grp_op: *,
infix_ap: x f y,
all: ∀x:A. B[x]
Lemmas referenced :
grp_inv_thru_op,
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,
axiomEquality,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:Perm(T)]. (inv\_perm(a O b) = inv\_perm(b) O inv\_perm(a))
Date html generated:
2016_05_16-AM-07_29_18
Last ObjectModification:
2015_12_28-PM-05_36_40
Theory : perms_1
Home
Index