Nuprl Lemma : perm_mon_ident
∀[T:Type]. ∀[a:Perm(T)]. ((a O id_perm() = a ∈ Perm(T)) ∧ (id_perm() O a = a ∈ Perm(T)))
Proof
Definitions occuring in Statement :
comp_perm: comp_perm,
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,
subtype_rel: A ⊆r B,
igrp: IGroup,
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_id: e,
infix_ap: x f y,
and: P ∧ Q,
all: ∀x:A. B[x]
Lemmas referenced :
mon_ident,
perm_igrp_wf,
igrp_wf,
perm_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
isect_memberEquality,
productElimination,
independent_pairEquality,
axiomEquality,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:Perm(T)]. ((a O id\_perm() = a) \mwedge{} (id\_perm() O a = a))
Date html generated:
2016_05_16-AM-07_29_22
Last ObjectModification:
2015_12_28-PM-05_36_22
Theory : perms_1
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