Nuprl Lemma : perm_grp_inv_id
∀T:Type. (inv_perm(id_perm()) = id_perm() ∈ Perm(T))
Proof
Definitions occuring in Statement :
inv_perm: inv_perm(p),
id_perm: id_perm(),
perm: Perm(T),
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
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_id: e
Lemmas referenced :
grp_inv_id,
perm_igrp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
universeEquality
Latex:
\mforall{}T:Type. (inv\_perm(id\_perm()) = id\_perm())
Date html generated:
2016_05_16-AM-07_29_15
Last ObjectModification:
2015_12_28-PM-05_36_43
Theory : perms_1
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