Nuprl Lemma : perm_igrp_wf
∀[T:Type]. (perm_igrp(T) ∈ IGroup)
Proof
Definitions occuring in Statement :
perm_igrp: perm_igrp(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
igrp: IGroup
Definitions unfolded in proof :
perm_igrp: perm_igrp(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
infix_ap: x f y,
assoc: Assoc(T;op),
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
prop: ℙ,
squash: ↓T,
ident: Ident(T;op;id),
cand: A c∧ B,
inverse: Inverse(T;op;id;inv)
Lemmas referenced :
mk_igrp_wf,
perm_wf,
comp_perm_wf,
id_perm_wf,
inv_perm_wf,
iff_weakening_equal,
perm_assoc,
true_wf,
squash_wf,
equal_wf,
perm_ident,
perm_inverse
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
universeEquality,
extract_by_obid,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
lambdaEquality,
independent_isectElimination,
isect_memberEquality,
independent_functionElimination,
productElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
because_Cache,
cumulativity,
imageElimination,
applyEquality,
isect_memberFormation,
lambdaFormation,
independent_pairEquality,
independent_pairFormation
Latex:
\mforall{}[T:Type]. (perm\_igrp(T) \mmember{} IGroup)
Date html generated:
2019_10_16-PM-00_59_06
Last ObjectModification:
2018_09_26-PM-08_09_08
Theory : perms_1
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